Coordinate Geometry Class 9 Worksheet have been designed as per the latest pattern for CBSE, NCERT and KVS for Grade 9. Students are always suggested to solve printable worksheets for Mathematics Coordinate Geometry Grade 9 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 9 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 9 for benefit of students and is available for free download.

## Mathematics Coordinate Geometry Worksheets for Class 9

We have provided **chapter-wise worksheets for class 9 Mathematics Coordinate Geometry** which the students can download in Pdf format for free. This is the best collection of Mathematics Coordinate Geometry standard 9th worksheets with important questions and answers for each grade 9th Mathematics Coordinate Geometry chapter so that the students are able to properly practice and gain more marks in Class 9 Mathematics Coordinate Geometry class tests and exams.

### Chapter-wise Class 9 Mathematics Coordinate Geometry Worksheets Pdf Download

1. Cartesian System

2. Plotting a Point in the Plane with given Coordinates

**•** Coordinate Geometry: The branch of mathematics in which geometric problems are solved

through algebra by using the coordinate system is known as coordinate geometry.**•** Coordinate System: Coordinate axes: The position of a point in a plane is determined with

reference to two fixed mutually perpendicular lines, called the coordinate axes.

In this system, position of a point is described by ordered pair of two numbers.**• Ordered pair:** A pair of numbers a and b listed in a specific order with ‘a’ at the first place and ‘b’ at the second place is called an ordered pair (a,b)

Note that (a, b) ¹ (b, a)

Thus (2,3) is one ordered pair and (3,2) is another ordered pair.

In given figure O is called origin.

The horizontal line X1

OX is called the X-axis.

The vertical line YOY’ is called the Y-axis.

P(a,b) be any point in the plane. ‘a’ the first number denotes the distance of point from Y-axis and ‘b’ the second number denotes the distance of point from X-axis.

a – X – coordinate | abscissa of P.

b – Y – coordinate | ordinate of P.

The coordinates of origin are (0,0)

Every point on the x-axis is at a distance o unit from the X-axis. So its ordinate is 0.

Every point on the y-axis is at a distance of unit from the Y-axis. So, its abscissa is 0.

Note: Any point lying on X- axis or Y – axis Y-axis does not lie in any quadrant

**Question.****Point (– 10, 0) lies**

(A) on the negative direction of the x-axis

(b) on the negative direction of the y-axis

(c) in the third quadrant

(d) in the fourth quadrant

**Answer**

A

**Question.** Signs of the abscissa and ordinate of a point in the second quadrant are respectively

(a) +, +

(b) –, –

(c) –, +

(d) +, –

**Answer**

C

**Question.****Point (0, –7) lies**

(a) on the x–axis

(b) in the second quadrant

(c) on the y-axis

(d) in the fourth quadrant

**Answer**

C

**Question.****Abscissa of all the points on the x-axis is**

(a) 0

(b) 1

(c) 2

(d) any number

**Answer**

D

**Question.** The points (–5, 2) and (2, – 5) lie in the

(a) same quadrant

(b) II and III quadrants, respectively

(c) II and IV quadrants, respectively

(d) IV and II quadrants, respectively

**Answer**

C

**Question.****Ordinate of all points on the x-axis is**

(a) 0

(b) 1

(c) – 1

(d) any number

**Answer**

A

**Question.****Point (–3, 5) lies in the**

(a) first quadrant

(b) second quadrant

(c) third quadrant

(d) fourth quadrant

**Answer**

B

**Question.****The point at which the two coordinate axes meet is called the**

(a) abscissa

(b) ordinate

(c) origin

(d) quadrant

**Answer**

C

**Question.** Points (1, – 1), (2, – 2), (4, – 5), (– 3, – 4)

(a) lie in II quadrant

(b) lie in III quadrant

(c) lie in IV quadrant

(d) do not lie in the same quadrant

**Answer**

D

**Question.** If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has

(a) x coordinate = – 5

(b) y coordinate = 5 only

(c) y coordinate = – 5 only

(d) y coordinate = 5 or –5

**Answer**

D

**Question.** A point both of whose coordinates are negative will lie in

(a) I quadrant

(b) II quadrant

(c) III quadrant

(d) IV quadrant

**Answer**

C

**Question.** On plotting the points O (0, 0), A (3, 0), B (3, 4), C (0, 4) and joining OA, AB, BC and CO which of the following figure is obtained?

(a) Square

(b) Rectangle

(c) Trapezium

(d) Rhombus

**Answer**

B

**Question.****If the coordinates of the two points are P (–2, 3) and Q (–3, 5), then (abscissa of P) –(abscissa of Q) is**

(a) – 5

(b) 1

(c) – 1

(d) – 2

**Answer**

B

**Question.****The perpendicular distance of the point P (3, 4) from the y -axis is**

(a) 3

(b) 4

(c) 5

(d) 7

**Answer**

A

**Question.** If P (5, 1), Q (8, 0), R (0, 4), S (0, 5) and O (0, 0) are plotted on the graph paper, then the point(s) on the x-axis are

(a) P and R

(b) R and S

(c) Only Q

(d) Q and O

**Answer**

D

**Question.****If y – coordinate of a point is zero, then this point always lies**

(a) in I quadrant

(b) in II quadrant

(c) on x- axis

(d) on y- axis

**Answer**

C

**Question.****Abscissa of a point is positive in**

(a) I and II quadrants

(b) I and IV quadrants

(c) I quadrant only

(d) II quadrant only

**Answer**

B

**Question.** If P (– 1, 1), Q (3, – 4), R (1, –1), S (–2, –3) and T (– 4, 4) are plotted on the graph paper, then the points in the fourth quadrant are

(a) P and T

(b) Q and R

(c) Only S

(d) P and R

**Answer**

B

**Question.****The points whose abscissa and ordinate have different signs will lie in**

(a) I and II quadrants

(b) II and IV quadrants

(c) I quadrant Only

(d) II and IV quadrants only

**Answer**

D

**Question.****The point whose ordinate is 4 and which lies on y-axis is**

(a) (4, 0)

(b) (0, 4)

(c) (1, 4)

(d) (4, 2)

**Answer**

B

**Question.****Which of the points P (0, 3), Q (1, 0), R (0, – 1), S (–5, 0), T (1, 2) do not lie on the x -axis?**

(a) P and R only

(b) Q and S only

(c) P, R and T

(d) Q, S and T

**Answer**

C

**Question.** In Fig. 3.2, the point identified by the coordinates (–5, 3) is

(a) T

(b) R

(c) L

(d) S

**Answer**

A

**Question.****The point which lies on y-axis at a distance of 5 units in the negative direction of yaxis is**

(a) (0, 5)

(b) (5, 0)

(c) (0, – 5)

(d) (– 5, 0)

**Answer**

C

**Question.****In Fig. 3.1, coordinates of P are**

(a) (– 4, 2)

(b) (–2, 4)

(c) (4, – 2)

(d) (2, – 4)

**Answer**

B

**Question.****Write whether the following statements are True or False? Justify your answer.****(i) Point (3, 0) lies in the first quadrant.****(ii) Points (1, –1) and (–1, 1) lie in the same quadrant.****(iii) The coordinates of a point whose ordinate is -1/2 and abscissa is 1 are (-1/2,1)****(iv) A point lies on y-axis at a distance of 2 units from the x-axis. Its coordinate are (2, 0).****(v) (–1, 7) is a point in the II quadrant.****Answer.** (i) The point (3, 0) has abscissa 3, the x-coordinate and ordinate is 0. If the ordinate of a point is zero, the point lies on the x-axis.

Hence, the given statement is false.

(ii) The point (1, –1) lies in IV quadrant and the point (–1, 1) lies in II quadrant.

Hence, the given statement is false.

(iii) We know that in the coordinates of a point, the abscissa comes first and then the ordinate. So, the coordinate of a point are (1,-1/2) and not (-1/2,1)

(iv) Any point which lies on the y-axis is of the form (0, y).

Hence, the given statement is false.

(v) In the II quadrant, signs of abscissa and ordinate are –, + respectively.

Hence, the statement that (–1, 7) is a point in the II quadrant is a true statement.

**Question.****Without plotting the points indicate the quadrant in which they will lie, if****(i) ordinate is 5 and abscissa is – 3****(ii) abscissa is – 5 and ordinate is – 3****(iii) abscissa is – 5 and ordinate is 3****(iv) ordinate is 5 and abscissa is 3****Answer.** (i) In the point (–3, 5) abscissa is negative and ordinate is positive, so it lies in the second quadrant.

(ii) In the point (–5, –3) abscissa and ordinate both are negative, so it lies in the third quadrant.

(iii) In the point (–5, 3) abscissa is negative and ordinate is positive, so it lies in the second quadrant.

(iv) In the point (3, 5) abscissa and ordinate both are positive, so it lies in the first quadrant.

**Question.** Plot the following points and write the name of the figure obtained by joining them in order: P (– 3, 2), Q (– 7, – 3), R (6, – 3), S (2, 2)**Answer.** Let X’OX and Y’OY be the coordinate axes. Then, the four points may be plotted as given below:

**Question.** Plot the points (x, y) given by the following table:

**Answer. **Let X’OX and Y’OY be the coordinate axes. Then, the given points may be plotted as given below:

**Question.****Plot the following points and check whether they are collinear or not:(i) (1, 3), (– 1, – 1), (– 2, – 3)**

**(ii) (1, 1), (2, – 3), (– 1, – 2)**

**(iii) (0, 0), (2, 2), (5, 5)**

Answer. (i)

Answer. (i)

From the graph, we find that all the three points lie on the same straight line. Hence, the given points are collinear.

From the graph, we find that all the three points do not lie on the same straight line. Hence, the given points are not collinear.

From the graph, we find that all the three points lie on the same straight line. Hence, the given points are collinear.

**Question.****Write the coordinates of each of the points P, Q, R, S, T and O from the Fig. 3.5.**

**Answer.** The coordinates of the points P, Q, R, S, T and O are P (1, 1), Q (–3, 0), R (–2, –3), S (2, 1), T (4, –2) and O (0, 0)

**Question.****In Fig. 3.6, LM is a line parallel to the y-axis at a distance of 3 units.****(i) What are the coordinates of the points P, R and Q?****(ii) What is the difference between the abscissa of the points L and M?**

**Answer. **(i) Clearly, the distance of P from y-axis is 3 units and that of from x-axis is 2 units. Since P lies in the first quadrant, so its coordinate are (3, 2). Point R lies on x-axis and its distance from y and x-axes are 3 and 0 units respectively. So, its coordinates are (3, 0). Clearly, point Q lies in the fourth quadrant. The distance of Q from y-axis is 3 units and from x-axis is 1 unit. So, the coordinates of Q (3, –1).

(ii) From the given figure (graph), we find that the points L and M lie on the same straight line. So, L and M are collinear.

Hence, the difference between the abscissa of the points L and M is 0.

**Question.****Plot the points P (1, 0), Q (4, 0) and S (1, 3). Find the coordinates of the point R such that PQRS is a square.****Answer.** Plot the points P (1, 0), Q (4, 0) and S (1,3) in the Cartesian plane. As we know all the sides of a square are equal and each angle is of 90o measure. Therefore, the abscissa of the vertex R is 4 and its ordinate is 3.

Hence, the coordinate of the point R are (4, 3).

**Question.****Which of the following points lie on y-axis?****A (1, 1), B (1, 0), C (0, 1), D (0, 0), E (0, – 1), F (– 1, 0), G (0, 5), H (– 7, 0), I (3, 3).****Answer. **We know that if a point lies on the y-axis, its abscissa is 0 and its ordinate is the y-value and its coordinate are (0, y).

Hence, C (0, 1), E (0, –1), G (0, 5) are the points which lie on y-axis.

**Question.** Plot the points (x, y) given by the following table. Use scale 1 cm = 0.25 units

**Answer.** Let X’OX and Y’OY be the coordinate axes. Then, the given points may be plotted as given below:

**Question.****A point lies on the x-axis at a distance of 7 units from the y-axis. What are its coordinates? What will be the coordinates if it lies on y-axis at a distance of –7 units from x-axis?****Answer.** The given points lies on the x-axis. The distance of this points from y-axis is 7 units and from x-axis is 0. So, its coordinates are (7, 0).

If it lies on y-axis, then the distance of it from y-axis is 0 and that of from x-axis is 7 units.

So, its coordinates are (0, 7).

**Question.** In which quadrant or on which axis each of the following points lie?**(– 3, 5), (4, – 1), (2, 0), (2, 2), (– 3, – 6)****Answer. **(i) (– 3, 5) lies in II quadrant.

(ii) (4, – 1) lies in IV quadrant.

(iii) (2, 0) lies in x-axis.

(iv) (2, 2) lies in first quadrant.

(v) (– 3, – 6) lies in the third quadrant.

**Question.****Taking 0.5 cm as 1 unit, plot the following points on the graph paper:****A (1, 3), B (– 3, – 1), C (1, – 4), D (– 2, 3), E (0, – 8), F (1, 0)****Answer** Let X’OX and Y’OY be the coordinate axes. Then, the given points may be plotted as given below:

**Question.** Points A (5, 3), B (– 2, 3) and D (5, – 4) are three vertices of a square ABCD. Plot these points on a graph paper and hence find the coordinates of the vertex C.**Answer.** Plot the points A (5, 3), B (– 2, 3) and D (5, – 4). Join AB and AD. As ABCD is a square, so all its sides are equal and each angle is of 90o measure. Therefore, the abscissa of the vertex C will be – 2 and ordinate – 4. Hence, the coordinates of the vertex C are (–2, –4).

**Question.** Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units respectively, one vertex at the origin, the longer side lies on the x-axis and one of the vertices lies in the III quadrant.**Answer.** As the length and breadth of the rectangle are 5 and 3 units respectively, one vertex at the origin, the longer side lies on the x-axis and one of the vertices lies in the III quadrant, so the coordinate of the vertices of rectangle OABC are O(0, 0), A (-5, 0), B (-5, -3) and C (0, -3).

**Question.****Find the coordinates of the point****(i) which lies on x and y axes both.****(ii) whose ordinate is – 4 and which lies on y-axis.****(iii) whose abscissa is 5 and which lies on x-axis.****Answer.** (i) The coordinates of the point which lies on both the axes are (0, 0).

(ii) The coordinates of the point whose ordinate is – 4 and which lies on y-axis are (0, –4).

(iii) The coordinate of the point whose abscissa is 5 and which lies on x-axis are (5, 0).

**Question.****From the given figure, answer the following;**

**(i) Write the points whose abscissa is 0.(ii) Write the points whose ordinate is 0.(iii) Write the points whose abscissa is – 5. **

**Answer.**(i) Clearly, the distance of points A, L and O from y-axis is 0. So, A (0, 3), L (0, -4) and O (0,

0) are the points whose abscissa is 0.

(ii) Clearly, the distance of points G, I and O from x-axis is 0. So, G (5, 0), I (-2, 0) and O (0,0) are the points whose ordinate is 0.

(iii) Clearly, the distance of points H and D from y-axis is 5 units and both lien in second and third quadrants respectively. So, (-5, -3) and D (-5, 1) are the points whose abscissa is -5.

**Question.****Plot the points A (1, – 1) and B (4, 5)****(i) Draw a line segment joining these points. Write the coordinates of a point on this line segment between the points A and B.****(ii) Extend this line segment and write the coordinates of a point on this line which lies outside the line segment AB.****Answer.** (i) M (2, 1) is a point on this line segment between the points A and B.

(ii) N (5, 7) is a point on this line which lies outside the line segment AB.

Mathematics Coordinate Geometry Worksheets for Class 9 as per CBSE NCERT pattern

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- CBSE Class 9 Mathematics Coordinate Geometry Workbook will surely help to improve knowledge of this subject

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