Worksheets For Class 10 Mathematics Coordinate Geometry

Coordinate Geometry Class 10 Worksheets have been designed as per the latest pattern for CBSE, NCERT and KVS for Grade 10. Students are always suggested to solve printable worksheets for Mathematics Coordinate Geometry Grade 10 as they can be really helpful to clear their concepts and improve problem solving skills. We at worksheetsbag.com have provided here free PDF worksheets for students in standard 10 so that you can easily take print of these test sheets and use them daily for practice. All worksheets are easy to download and have been designed by teachers of Class 10 for benefit of students and is available for free download.

Mathematics Coordinate Geometry Worksheets for Class 10

We have provided chapter-wise worksheets for class 10 Mathematics Coordinate Geometry which the students can download in Pdf format for free. This is the best collection of Mathematics Coordinate Geometry standard 10th worksheets with important questions and answers for each grade 10th Mathematics Coordinate Geometry chapter so that the students are able to properly practice and gain more marks in Class 10 Mathematics Coordinate Geometry class tests and exams.

Chapter-wise Class 10 Mathematics Coordinate Geometry Worksheets Pdf Download

Question. The centre of a circle is C(2, k). If A(2, 1) and B(5, 2) are two points on its circumference, then the value of k is   
(A) 6
(B) 2
(C) –6
(D) –2

Question. The ratio in which the line joining (1, 3) an (2, 7) is divided by 3x + y = 9 is   
(A) 3 : 4
(B) 2 : 4
(C) 1 : 2
(D) 3 : 1

Question. The distance between the points (2k + 4, 5k) and (2k, –3 + 5k) in units is   
(A) 1
(B) 2
(C) 4
(D) 5

Question. The distance between the points (3k + 1, –3k) and (3k – 2, –4 –3k) (in units) is   
(A) 3k
(B) 5k
(C) 5
(D) 3

Question. The point which divides the line joining the points A(1, 2) and B(–1, 1) internally in the ratio 1 : 2 is _________.   
(A) (-1/5 ,5/3)
(B) (1/3 , 5/3)
(C) (–1, 5)
(D) (1, 5)

Question. The ratio in which the line joining (a + b, b + a) and (a – b, b – a) is divided by the point (a, b) is ___________.   
(A) b : a internally
(B) 1 : 1 internally
(C) a : b externally
(D) 2 : 1 externally

Question. If the line (3x -8y+5) +a(5x-3y +10) = 0 is parallel to X-axis, then a is   
(A) -(8/3)
(B) -(3/5)
(C) –2
(D) 1/2

Question. Find the area of a triangle formed by the lines 4x-y-8 = 0, 2x+y-10 = 0 and y = 0 (in sq units). 
(A) 5
(B) 6
(C) 4
(D) 

Question. Find the length of the longest side of the triangle formed by the line 3x + 4y =12with the coordinate axes.   
(A) 9
(B) 16
(C) 5
(D) 7

Question. Find the area of the triangle formed by the line 3x – 4y +12 = 0with the coordinate axes.   
(A) 6 units2
(B) 12 units2
(C) 1 units2
(D) 36 units2

Question. Find the equation of a line which divides the line segment joining the points (1, 1) and (2, 3) in the ratio 2 : 3 perpendicularly,   
(A) 5x – 5y + 2 = 0
(B) 5x + 5y + 2 = 0
(C) x + 2y – 5 = 0
(D) x + 2y + 7 = 0

Question. If A(-2,3) and B(2,3) are two vertices of ΔABCand G(0, 0) is its centroid, then the coordinates of C are 
(A) (0,-6)
(B) (-4,0)
(C) (4,0)
(D) (0,6)

Question. Let ΔABCbe a right angled triangle in which A(0, 2) and B(2, 0). Then the coordinates of C can be   
(A) (0, 0)
(B) (2, 2)
(C) either (A) or (B)
(D) none of these

Question. If ΔABCis a right angled triangle in which A(3, 0) and B(0, 5), then the coordinates of C can be   
(A) (5, 3)
(B) (3, 5)
(C) (0, 0)
(D) both (B) and (C)

Question. A triangle is formed by the lines x – y – 8,X-axis and Y-axis. Find its centroid.   
(A) (8/3 , 8/3 )
(B) (8, 8)
(C) (4, 4)
(D) (0, 0)

VERY SHORT ANSWER TYPE QUESTIONS

Question. If the distance between the points (x, 0) and (5, 8) is 10 units, find the value(s) of x.

Question. What is the distance of the point A(3, –4) from y-axis?

Question. In what ratio is the line joining the points P(7, 7) and Q(–4, 4) is divided by (0, –1)?

Question. What are the coordinates of the centroid of triangle formed by points A(–2, 4), B(7, –3) and C(1, 5).

Question. Find the coordinates of points which divides line joining (–4, 0) and (0, 6) in the ratio 1 : 3. 

Question. Point A(3, –4) lies on circle of radius 5 cm with centre (0, 0). Write the coordinates of the other end of the diameter whose one end is A.

Question. Find the third vertex of a triangle if two of its vertices are (3, –6) and (–5, 2) and its centroid is at the point (2, 0).

Question. What is the distance between the points (1, –2) and (–3, 2)?

Question. What is the area of triangle formed by the points (–2, 0), (4, 0) and (2, 3).

Question. Find the mid-point of the line segment joining the points P(–3, 4) and Q (9, –6).

Question. C is point on the perpendicular bisector of AB. What is the relation between A, B, C?

Question. What is the ordinate of any point on x-axis?

Question. Find the coordinates of fourth vertex of the rectangle formed by the points (0, 0), (3, 0) and (0, 5).

Question. What is the distance of the point (–6, 8) from origin?

Question. What is the area of ΔABC, if points A, B and C are collinear?

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set A

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set B

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set C

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set D

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set E

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set F

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set G

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set H

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set I

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set J

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set K

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set L

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set M

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set O

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set P

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set Q

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set R

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set S

CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set T

CBSE Class 10 Mathematics Coordinate Geometry Worksheets Set A

CBSE Class 10 Mathematics Coordinate Geometry Worksheets Set B

CBSE Class 10 Mathematics Coordinate Geometry Worksheets Set D

CBSE Class 10 Mathematics Coordinate Geometry Worksheets Set E

CBSE Class 10 Mathematics Coordinate Geometry Worksheets Set F

CBSE Class 10 Mathematics Coordinate Geometry Worksheets Set G

CBSE Class 10 Mathematics Coordinate Geometry Worksheets Set H

Question. Use distance formula to show that the points A (- 2,3), B (1, 2) and C (7,0) are collinear. 
Solution.

Question. In what ratio does the line segment joining the points (6, 4) and (1, –7) is divided internally by the axis of x?
Solution. 4 : 7

Question. Find the coordinates of the point of trisection of the line segment AB whose end points are A (2, 1) and B (5, –8).
Solution. (3, –2) and (4, –5)

Question. Find the length of median AD of a triangle whose vertices are A(–1, 3), B(1, –1) and C(5, 1).
Solution. 5 units

Question. Find the area of the quadrilateral, the coordinates of whose vertices are (1, 2), (6, 2), (5, 3) and (3, 4).
Solution. 11/2 sq.units

Question. What point on x-axis is equidistant from the points (–3, 4) and (7, 6)?
Solution. (3, 0)

Question. The coordinates of the centroid of a triangle are (1, 3) and the two vertices are (8, 5) and (–7, 6). Find the third vertex of the triangle.
Solution. (2, –2)

Question. If (3, 2), (4, 4) and (1, 3) are the mid-points of the sides of a triangle, find the coordinates of the vertices of the triangle.
Solution. (0, 1), (6, 3) and (2, 5)

Question. Three vertices of a parallelogram, taken in order are (3, 1), (2, 2) and (–2, 1) respectively. Find the coordinates of fourth vertex.
Solution. (–1, 0)

Question. Find the ratio in which the y-axis divides the segment joining (-3,6) and(12,-3).
Solution. 1/4

Question. Find the value of x for which the distance between the points P(4,-5) and Q ( 12 , x ) i s10 units.
Solution. 1, -11

Question. If the points A (4,3) and B(x,5) are on the circle with Centre O(2,3) then find the value of x.
Solution. 2

Question. What is the distance between the point A(c,0) and B(0,-c)?
Solution. √2 c

Question. For what value of p, are the points (-3,9),(2,p) and(4,-5) collinear?
Solution. -1

Question. Find the ratio in which the point P (x,2) divides the line-segments joining the points A(12,5)and B(4,- 3).Also ,find the value of x.
Solution. 3:5, x=9

Question. If the points A (-2, 1),B (a, b) and C(4,-1) are collinear and a-b=1.Find the value of a and b.
Solution. a=1, b=0

Question. In what ratio does the point (-4, 6) divides the line segment joining the points A (-6, 10)
Solution. 2/7

Question. Show that the points (3,2),(0,5),(-3,2) and (0,-1) are the vertices of a square.
Solution. Proof

Question. Point P divides the line segment joining the points A (2,1) and B(5,-8) such that AP:
AB=1:3 If P lies on the line2x-y+k=0, then find the value of k.
Solution. K=-8

Question. If the distance between the points (4,p) &(1,0) is 5, then find the value of p.
Solution. ±4

Question. If the point A(1,2), B(0,0) and C(a ,b) are collinear, then find the relation between a and b.
Solution. 2a=b

Question. Find the ratio in which the Y-axis divides the line segment joining the points (5,-6) and (-1,-4). Also find the coordinates of the point of division.
Solution. 5:1, (0,-13/3)

Question. Find the distance between the points P (7,5) and Q(2,5).
Solution. 5

Question. If P (α/3 ,4) is the midpoint of the line segment joining the points Q(-6,5) and R( -2,3),then find the value of α.
Solution. -12

Question. By distance formula, show that the points (1,-1), (5,2) and (9,5) are collinear.
Solution. Proof

Question. Find the relation between x and y if the points(2,1),(x , y)and(7,5) are collinear
Solution. 4x – 5y – 3=0

Question. Find the ratio in which the line2x+3y=10 divides the line segment joining the points (1,2) and (2,3).
Solution. 2:3

Question. Show that the mid-point of the line segment joining the points (5, 7) and (3, 9) is also the mid-point of the line segment joining the points (8, 6) and (0, 10). 
Solution. Let A(5, 7), B(3, 9), C(8, 6) and D(0, 10) be the given points. Therefore,by mid-point formula,we have,
Coordinates of the mid-point of AB are

Coordinates of the mid-point of CD are

Therefore, the mid-point of AB = mid point of CD.

Question. What is the distance between the points A(c,0) and B(0, – c)? 
Solution.

Question. Find the point on the x-axis which is equidistant from (2,-5) and (-2,9) (4) 
Solution. Let the point of x-axis be P(x, 0)
Given A(2, -5) and B(-2, 9) are equidistant from P
That is PA = PB
Hence PA² = PB² → (1)

Question. If (5,2), (- 3,4) and (x, y ) are collinear, show that x + 4y – 13 = 0. 
Solution. Since the points are collinear
The area of triangle = 0
∴ Area of triangle =0

Question. If the mid-point of the line joining (3,4) and (k, 7) is (x, y) and 2x + 2y + 1 = 0 find the value of k.   
Solution.

Question. If the point C(-1, 2) divides the line segment AB in the ratio 3 : 4, where the coordinates of A are (2, 5), find the coordinates of B.   
Solution. Given: A (2,5) and C(-1,2)
Let the coordinate of the point B be (a,b).
it is given that AC : BC = 3:4
Then, by section formula , coordinates of C are given by

Question. The three vertices of a parallelogram ABCD taken in order are A (-1, 0), B(3, 1) and C(2, 2). Find the height of a parallelogram with AD as its base.   
Solution.

Question. Find the coordinates of the point on y-axis which is nearest to the point (- 2, 5). 
Solution. The point on y-axis that is nearest to the point(-2,5) is (0,5).

Question. If 18, a ,b ,- 3 are in A.P., then find a + b. 
Solution. Since 18, a, b, and – 3 are in A.P., Then
a – 18 = – 3 – b
or, a + b = – 3 + 18
or, a + b = 15

Question. The points A (x₁,y₁), B (x₂, y₂) and C (x₃, y₃) are the vertices of ΔABC.   
Solution. A(x₁, y₁), B(x₂, y₂), C(x₃, y₃) are the three vertices of ΔABC.
i. The median from A meets BC at D. Find the coordinates of the point D.

ii. Find the coordinates of the point P on AD such that AP : PD = 2:1.

iii. Find the points of coordinates Q and R on medians BE and CP respectively such that BQ : QE = 2 :1 and CR : RP = 2 :1.

iv. What are the coordinates of the centroid of the triangle ABC? 

Question. Find the radius of the circle whose end points of diameter are (24,1) and (2,23)]   
Solution. (x₁, y₁) = (24,1) and (x₂, y₂) = (2,23)

Question. Find the coordinates of the points Q on the x–axis which lies on the perpendicular bisector of the line segment joining the points A(–5, –2) and B(4, –2). Name the type of triangle formed by the points Q, A and B.   
Solution. Let Q(x, 0) be a point on x–axis which lies on the perpendicular bisector of AB.
Therefore, QA = QB
⇒ QA² = QB²
⇒ (–5 – x)² + (–2 – 0)² = (4 – x)2 + (–2 – 0)²
⇒ (x + 5)² + (–2)² = (4 – x)² + (–2)²
⇒ x² + 25 + 10x + 4 = 16 + x² – 8x + 4
⇒ 10x + 8x = 16 – 25
⇒ 18x = –9
⇒ x = -9/18 -1/2

Question. Find the ratio in which the line segment joining the points A(3, – 3) and B(- 2,7) is divided by the x-axis. Also, find the coordinates of the point of division.   
Solution.. According to the question,
A (3,-3) and B (- 2, 7)
On the x-axis, the y-coordinate is zero
So, let the point be (x, 0)
Let the ratio be k : 1

Question. Find the distance between the following pairs of points: (2, 3), (4,1)   
Solution. Applying Distance Formula to find distance between points (2, 3) and (4,1), we get

Question. Find the distance between the following pairs of points: (a, b), (-a, -b) 10
Solution. Applying Distance Formula to find distance between points (a, b) and (-a, -b), we get

Question. In what ratio does the point C(4, 5) divide the join of A(2, 3) and B(7, 8)?
Solution. Let the point C(4, 5) divides the join of A(2, 3) and B(7, 8) in the ratio k:1

Thus, C divides AB in the ratio 2:3

Question. Find the value(s) of p, if the points A(2, 3), B(4, k), C(6, – 3) are collinear.
Solution. Let the points A (2, 3), B (4,k) and C (6 -3) be collinear.
If the points are collinear then area of triangle ABC formed by these three points is 0.

Question. Show that quadrilateral PQRS formed by vertices P(22,5), Q(7,10), R(12,11) and S(3,24) is not a parallelogram.
Solution. Given vertices of quadrilateral are P(22, 5), Q(7, 10), R(12, 11) and S(3, 24).

Hence, given vertices of a quadrilateral are not forming a parallelogram.

Question. Find the points X-axis which are at a distance of 2√5 from the point(7,-4). How many such points are there?
Solution. We have to find the points on X-axis which are at a distance of 2√5 from the
point(7,-4). Also,we will how many such points are there.
Let, the point on X-axis be (x,0).
Now, by using distance formula,

Question. Find the coordinates of the midpoint of the line segment joining A(3, 0) and B(-5, 4).
Solution. Mid-point of the line segment joining the points A(3, 0) and B(-5, 4)

Hence the coordinate of mid point of line segment is (-1, 2).

Question. Show that the points A (2,-2), B(14,10), C (11, 13) and D(-1, 1) are the vertices of a rectangle.
Solution. According to the question, A (2,-2), B(14,10), C (11, 13) and D(-1, 1)

Question. Find the coordinates of the points which divide the line segment joining A(-2, 2) and B(2, 8) into four equal parts.
Solution. Let P (x1, y1) Q(x2, y2) and R(x3, y3) be the points which divide the line segment AB into four equal parts.

Question. Find the complement of the given angle.

Solution. Complement of the angle 20° = 90° – 20° = 70°

Question. Find the distance of the point P(6, -6) from the origin.
Solution. Let P(6, -6 ) be the given point and O(0, 0) be the origin.

Question. Find the distance between the points A and B in A(5, – 8), B (-7, – 3)
Solution.

Question. If the points A(1,-2), B(2,3), C(-3,2) and D(-4,-4) are the vertices of the parallelogram ABCD, then taking AB as the base, find the height of the parallelogram.

Solution. Let DM = h be the height of the parallelogram ABCD when AB is taken as the base.

Question. Find the area of the triangle whose sides are along the lines x = 2, y = 0 and 4x + 5y = 20.
Solution.

Question. Find the coordinates of points which trisect the line segment joining (1, -2) and (-3, 4).
Solution. Let A (1, -2) and B (-3,4) be the given points.
Let the points of trisection be P and Q. Then, AP = PQ = QB = X(say)

So, P divides AB internally in the ratio 1 : 2 while Q divides internally in the ratio 2: 1.
Thus, the coordinates of P and Q are

Hence, the two points of trisection are (-1/3, 0) and (-5/3, 2)

Question. Find the distance between the points P(-6, 7) and Q(-1, -5).
Solution. Here, x1 = -6, y1 = 7 and x2 = -1, y2 = -5
Therefore,by distance formula,we have,

PRACTICE EXERCISE

Question. A point P is at a distance of √13 units from the point (5, 4). Find the coordinates of P, if its ordinate is thrice of its abscissa.
Solution. (2,6) or (7/5 , 21/5)

Question. The area of a triangle is 5 square units. Two of its vertices are (2, 1) and (3, –2). The third vertex lies on y = x + 3. Find the third vertex.
Solution. (7/2 , 13/2) or ( -3/2 , 3/2)

Question. Show that the points A(2, –1), B(3, 4), C(–2, 3) and D(–3, –2) forms a rhombus but not a square. Find the area of the rhombus also.
Solution. 24 sq. units.

Question. Find the value of p if the distance between the points (3, p) and (4, 1) is 10 units.
Solution. p = 4 or –2

Question. Find the coordinates of the point which divides the line segment joining the points (4, –7) and (–5, 6) internally in the ratio 7 : 2.
Solution. (-3, -28/9)

Question. If the coordinates of two points A and B are (3, 4) and (5, –2) respectively. Find the coordinates of any point P, if PA = PB and area of ΔPAB = 10 square units.
Solution. (7, 2) or (1, 0)

Question. Find the coordinate of point P which divides the join of A(6, 5) and B(9, 2) in the ratio 1 : 2.
Solution. P(7, 4)

Question. If the coordinates of the mid-points of the sides of a triangle are (4, –3), (4, 5) and (–2, 3). Find the coordinates of its centroid.
Solution. (2 , 5/3)

Question. Find the area of the triangle whose vertices are :
(i) A (1, –1), B(–4, 6) and C(–3, –5) (ii) P (4, 2), Q(4, 5) and R (–2, 2)
(iii) A (1, 2), B(–2, 3) and C(–3, –4) (iv) P (5, 2), Q(4, 7) and R (7, –4)
Solution. (i) 24 sq. units (ii) 9 sq. units (iii) 11 sq. units. (iv) 2 sq. units

Question. A and B are the points (1, 2) and (2, 3). Find the coordinates of point C on the line segment AB such that 3AC = 4 BC.
Solution. C (11/7 ,18/7)

Question. Find the points of trisection of the line segment joining the points :
(i) (3, –2) and (–3, –4) (ii) (1, –2) and (–3, 4)
Solution. (i) (1 , -8/3 ) , (-1 , -10/3) (ii) (-1/3 , 0 ) , (-5/3 , 2)

Question. ABCD is a square with the opposite angular points A(3, 4) and C(1, –1). Find the coordinates of B and D.
Solution. (9/2 , 1/2) and (-1 /2 , 5/2)

Question. Find the coordinates of the circumcentre of a triangle whose vertices are A(5, 1), B(11, 1) and C(11, 9).
Solution. (8, 5)

Question. Three consecutive vertices of a parallelogram are (–2, –1), (1, 0) and (4, 3). Find the coordinate of the fourth vertex.
Solution. (1, 2)

Question. Find the value of y if the distance between the points (2, –3) and (10, y) be 10 units.
Solution. y = 3 or –9

Question. Find the ratio in which the point (11, 15) divides the line segment joining the points (15, 5) and (9, 20).
Solution. 2 : 1

Question. Find the value of x such that PQ = QR where the coordinates of P, Q and R are (6, –1), (1, 3) and (x, 8) respectively.
Solution. x = – 3 or 5

Question. Determine the ratio in which the line 3x + y – 9 = 0 divides the segment joining the points (1, 3) and (2, 7).
Solution. 3 : 4

Question. In what ratio the point (–3, k) divides the line segment joining the points (–5, –4) and (–2, 3). Hence, find the value of k.
Solution. 2 : 1; k = 2/3

Question. Find the ratio in which the line segment joining (–2, –3) and (5, 6) is divided by (i) x-axis (ii) y-axis. Also, find the coordinates of the point of division in each case.
Solution. (i) 1 : 2, (1/3 , 0) (ii) 2 : 5; (0,-3/7)

Question. If the coordinates of the mid-points of the sides of a triangle are (1, 2), (0, –1) and (2, –1). Find the coordinates of its vertices.
Solution. (1, –4), (3, 2) and (–1, 2)

Question. Find the point on x-axis which is equidistant from the points (–4, 6) and (5, 9).
Solution.(3, 0)

Question. Find the point on the y-axis which is equidistant from the points (3, 2) and (–5, –2).
Solution. (0, –2)

Question. The coordinates of the middle points D, E, F of the sides BC, CA and AB respectively of a ΔABC are (–3, 2), (5, –7) and (11, 7) respectively, find the coordinates of the vertices A, B and C.
Solution. (19, –2), (3, 16), (–9, –12)

Question. The line segment joining the points (–6, 8) and (8, –6) is divided into four equal parts. Find the coordinates of the point of section.
Solution. (-5/2 , 9/2);(1, 1) ;(9/2 , -5/2)

Question. For what value of x, the distance between P(x, 7) and Q(–2, 3) is 4 5 units.
Solution. x = 6 or –10

Question. Find the ratio in which the line-segment joining the points (6, 4) and (1, –7) is divided internally by x-axis.
Solution. 4 : 7

Question. The line joining the points (2, 1) and (5, –8) is trisected at the points P and Q. If P lies on the line 2x – y + k = 0, find the value of k. 
Solution. k = – 8 or – 13

Question. The centre of a circle is (3k + 1, 2k – 1). If the circle passes through the point (–1, –3) and the length of its diameter be 20 units, find the value of k.
Solution. k = 2, – 46/13

Question. If the points (10, 5), (8, 4) and (6, 6) are the mid-points of the sides of a triangle, find its vertices.
Solution. (8, 7), (12, 3), (4, 5)

Question. Find the coordinates of the points on the x-axis which are at a distance of 5 units from the point (5, 4).
Solution. (8, 0) and (2, 0)

Question. Find the coordinates of the points on the y-axis which are at a distance of 13 units from the point (12, 9).
Solution. (0, 14) and (0, 4)

Question. Two vertices of a triangle are (1, 2) and (3, 5) and its centroid is at the origin. Find the coordinates of the third vertex.
Solution. (–4, –7)

Question. A (3, 2) and B(–2, 1) are two vertices of ΔABC whose centroid G has the coordinates (5/3 , -1/3) Find the coordinates of the third vertex C of the triangle.
Solution. (4, –4)

Question. If the coordinates of the mid-points of the sides of a triangle are (1, 1), (2, –3) and (3, 4). Find its centroid.
Solution. (2 , 2/3)

Question. Find the ratio in which the line segment joining the points (7, 3) and (–4, 5) is divided internally by y-axis.
Solution. 7 : 4

Question. Find the centre of a circle, the end points of whose one diameter are (–3, –1) and (5, 8).
Solution. (1 , 7/2)

Question. Find the lengths of medians of a ΔABC having the vertices A(5, 1), B(1, 5) and C(–3, –1).
Solution. AD = √37 , BE = 5, CF = 2√13

Question. The line segment joining the points (3, –4) and (1, 2) is trisected at the ponts P and Q. If the coordinates of P and Q are (p, –2) and (5/3 , q) respectively, find the values of p and q.
Solution. p = 7/3 , q = 0

Question. (i) For what value of k, the points (k, –1), (5, 7) and (8, 11) are collinear?
(ii) For what value of k are the points (k, 2 – 2k), (–k + 1, 2k) and (–4 – k, 6 – 2k) lie on a straight line?
Solution. (i) k = – 1 (ii) k = – 1 or 1/2

Question. The vertices of some triangles are given below alongwith their areas. Find the value of a.
Vertices Area
(i) (2, 3), (6, –2), (–2, a) 6
(ii) (3, 8), (4, a), (5, –2) 8
Solution. (i) a = 5 or 11 (ii) a = – 5 or 11

Question. Find the distance between the points:
(i) A (–3, –2) and B (–6, –7)
(ii) P(a, 0) and Q(0, b)
(iii) A (–m, –n) and B (m, n)
(iv) R( 3 √1, 1) and S(0, 3)
(v) M(3√ 3, 3√ 3) and N(0, 0)
(vi) A (a sin α, – b cos α) and B (–a cos α, b sin α)
Solution.
(i) √34 units
(ii) √a2 + b2 units
(iii) √2 m2 + n2 units
(iv) 2√ 2 units
(v) 2 √6 units
(vi) √a2 + b2 (sin α + cosα)

Question. An equilateral triangle has two vertices at the points (0, 0) and (3, 3) . Find the coordinates of the third vertex.
Solution. (0, 2 √3) or (3, √ 3)

Question. Find the centroid of a triangle whose vertices are :
(i) (–2, 3), (2, –1), (4, 0) (ii) (4, –8), (–9, 7), (18, 13)
Solution. (i)(4/3 , 2/3) (ii) (13/3 , 4)

Question. Find the coordinates of the points equidistant from three given points A(5, 1), B(–3, –7) and C(7, –1).
Solution. (2, –4)

Question. Find the coordinates of a point whose distance from (3, 5) is 5 units and that from (0, 1) is 10 units.
Solution. (6, 9)

Question. A circle passes through the points A(3, 1), B(1, –3) and C(6, –8). Find the coordinates of the centre of the circle.
Solution. (6, –3)

Question. The coordinates of a vertex of a triangle are (2, 5) and the coordinates of the mid-points of the sides passing through this vertex are (8, 0) and (9, 3). Find the coordinates of the remaining vertices.
Solution. (14, –5) and (16, 1)

Question. Find the coordinates of the point of intersection of medians of ΔABC whose vertices are A(–7, 5), B(– 1, –3) and C(5, 7).
Solution. (–1, 3)

Question. Find the area of the quadrilateral, the coordinates of whose vertices are :
(i) (–3, 2), (5, 4), (7, –6) and (–5, –4) (ii) (–4, –2), (–3, –5), (3, –2) and (2, 3)
(iii) (–5, 7), (–4, –5), (–1, –6) and (4, 5) (iv) (6, 9), (7,4), (4, 2) and (3, 7)
Solution. (i) 80 sq. units (ii) 28 sq. units (iii) 72 sq. units (iv) 17 sq. units

Question. If the area of the quadrilateral whose angular points, taken in order, are (1, 2), (–5, 6), (7, –4), (p, –2) be zero, find the value of p.
Solution. p = 3

Mathematics Coordinate Geometry Worksheets for Class 10 as per CBSE NCERT pattern

Parents and students are welcome to download as many worksheets as they want as we have provided all free. As you can see we have covered all topics which are there in your Class 10 Mathematics Coordinate Geometry book designed as per CBSE, NCERT and KVS syllabus and examination pattern. These test papers have been used in various schools and have helped students to practice and improve their grades in school and have also helped them to appear in other school level exams. You can take printout of these chapter wise test sheets having questions relating to each topic and practice them daily so that you can thoroughly understand each concept and get better marks. As Mathematics Coordinate Geometry for Class 10 is a very scoring subject, if you download and do these questions and answers on daily basis, this will help you to become master in this subject.

Benefits of Free Coordinate Geometry Class 10 Worksheets

1. You can improve understanding of your concepts if you solve NCERT Class 10 Mathematics Coordinate Geometry Worksheet,
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5. Will help you to quickly revise all chapters of Class 10 Mathematics Coordinate Geometry textbook
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These Printable practice worksheets are available for free download for Class 10 Mathematics Coordinate Geometry. As the teachers have done extensive research for all topics and have then made these worksheets for you so that you can use them for your benefit and have also provided to you for each chapter in your ebook. The Chapter wise question bank and revision worksheets can be accessed free and anywhere. Go ahead and click on the links above to download free CBSE Class 10 Mathematics Coordinate Geometry Worksheets PDF.