CBSE Class 9 Mathematics Coordinate Geometry Worksheet

Key concepts

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)

1. In which quadrant or on which axes do each point lies

a) The ordinate is 3 and abscissa is – 4

b) The abscissa is – 2 and ordinate is – 3

c) (- 3, 2)

d) (0, - 4)

e) (5, 0)

2. Given point P (3, 4). What is the distance of point P from (a) x axis (b) y axis?

3. Plot the points A (4, 0), B (4, 4) and C (0, 4) on the graph. Join OA, AB, BC, and CO. Name the figure so formed and measure its sides

4. How many axis and quadrants are there in a Cartesian plane?

5. Plot the points on a graph paper:

(a) (3, 4) (b) (-2, 3) (c) (-1,-2) (d) (5,-1)

6. Check wheat her the points (1, 5), (0, 3) lie on the line y = 3 + 2x or not

7. Find the area of the triangle whose vertices are (0, 4), (0, 0) and (2, 0) by plotting them on graph

8. Find the equation of a line parallel to x – axis at a distance of 2 units below x - axis

9. Find the coordinates of the point

(a) Which lies on x and y axis both

(b) Whose ordinate is – 4 and which lies on y axis

(c) Whose abscissa is 5 and which lies on x – axis

10. Write the coordinates of a point left of y – axis and on y – axis at a distance of 6 units

11. Draw the graph of the equation y = 3x

ASSERTION REASONING QUESTIONS

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R).
Mark the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion: The abscissa of a point (5, 2) is 5.
Reason: The perpendicular distance of a point from y-axis is called its abscissa.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true
Answer : We know that the perpendicular distance of a point from y-axis is called its x-coordinate or abscissa.
So, Reason is correct.
The x co-ordinate of the point (5, 2) is 5.
So, Assertion is also correct
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .

Question. Assertion : The point (0, 4) lies on y -axis.
Reason : The x co-ordinate on the point on y -axis is zero.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that the if the point lies on y-axis, its x-coordinate is 0.
So, Reason is correct.
The x co-ordinate of the point (0, 4) is zero.
So, Point (0, 4) lies on y -axis.
So, Assertion is also correct
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .

Question. Assertion : The point (-2, 0) lies on y -axis and (0, 4) on x -axis.
Reason : Every point on the x -axis has zero distance from x -axis and every point on the y -axis has zero distance from y -axis.
(a) Both assertion (A) and reason (R) are true and reason
(R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason
(R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that Every point on the x -axis has zero distance from x -axis and every point on the y -axis has zero distance from y -axis.
So, Reason is correct.
Now, point (-2, 0) lies on x-axis and (0, 4) on y-axis
So, Assertion is not correct
Correct option is (d) Assertion (A) is false but reason (R) is true.

Question. Assertion: Point (4, -2) lies in IV quadrant.
Reason: The perpendicular distance of a point from y-axis is called its abscissa.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that the perpendicular distance of a point from y-axis is called its x-coordinate or abscissa.
So, Reason is correct.
Point (4, -2) lies in IV quadrant.
So, Assertion is also correct but Reason is not the correct explanation of Assertion.
Correct option is (b) Both assertion (A) and reason
(R) are true and reason (R) is not the correct explanation of assertion (A) .

Question. Assertion : The points (-1, 2) and (2,- 1) are at different positions in the coordinate plane.
Reason : Point (-1, 2) lies in II-quadrant and (2,- 1) lies in IV quadrant
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that Point (-1, 2) lies in II-quadrant and (2,- 1) lies in IV quadrant
So, Reason is correct.
Hence the points (-1, 2) and (2,- 1) are at different positions in the coordinate plane.
So, Assertion is also correct
Correct option is (a) Both assertion (A) and reason
(R) are true and reason (R) is the correct explanation of assertion (A) .

Question. Assertion : If the ordinate of a point is equal to its abscissa, then the point lies either in the first quadrant or in the second quadrant.
Reason : A point both of whose coordinates are negative will lie in third quadrants.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that A point both of whose coordinates are negative will lie in third quadrants.
So, Reason is correct.
Also we know that If the ordinate of a point is equal to its abscissa, then the point lies either in the first quadrant or in the third quadrant.
So, Assertion is not correct
Correct option is (d) Assertion (A) is false but reason (R) is true.

Question. Assertion: The perpendicular distance of the point A(3, 4) from the y-axis is 4
Reason: The perpendicular distance of a point from y-axis is called its x-coordinate.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that the perpendicular distance of a point from y-axis is called its x-coordinate or abscissa.
So, Reason is correct.
The x co-ordinate of the point (3, 4) is 3.
So, Assertion is not correct
Correct option is (d) Assertion (A) is false but reason (R) is true.

Question. Assertion: Point A(-2, -4) lies on III quadrant
Reason: A point both of whose coordinates are negative lies in III quadrant
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that a point both of whose coordinates are negative lies in III quadrant
So, Reason is correct.
Hence, Point A(-2, -4) lies on III quadrant
So, Assertion is also correct and Reason explains Assertion
Correct option is (a) Both assertion (A) and reason (R) are true and reason
(R) is the correct explanation of assertion (A) .

Question. Assertion: A point whose abscissa is -3 and ordinate is 2 lies in second quadrant
Reason: Points of the type (–, +) lie in the second quadrant.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that Points of the type (–, +) lie in the second quadrant.
So, Reason is correct.
Hence, point whose abscissa is -3 and ordinate is 2 lies in second quadrant
So, Assertion is also correct and Reason explains Assertion
Correct option is (a) Both assertion (A) and reason (R) are true and reason
(R) is the correct explanation of assertion (A) .

Question. Assertion: A point whose abscissa is 2 and ordinate is -3 lies in fourth quadrant
Reason: Points of the type (–, +) lie in the second quadrant.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that Points of the type (–, +) lie in the second quadrant.
So, Reason is correct.
Also, we know that Points of the type (+, –) lie in the fourth quadrant.
Hence, point whose abscissa is 2 and ordinate is -3 lies in fourth quadrant
So, Assertion is also correct but Reason is the not the correct explanation of Assertion.
Correct option is (b) Both assertion (A) and reason (R) are true but reason
(R) is not the correct explanation of assertion (A) .

1. Write the coordinates of a point which:-
(a) Lies on the x-axis and is at a distance of 4 units to the right of the origin.
(b) Lies on the y-axis and is at a distance of y units below the x-axis.
(c) Is at a distance of 3 units from the x-axis and 7 units from the y-axis. [there would be four such points]

2. Draw the graphs of the eqs:-
(a) 3x – 2y = 7 (b) y = - 2
on the same pair of axes. Read the coordinates of their point of intersection.

3. Find the point where the line represented by the equation 5y – 3x – 10 = 0 cuts the y-axis.

4. Draw the graph of the line 3x + 4y = 18. With the help of graph find value of y when x = 2. (show this point on the graph)

5. On a graph draw a quadrilateral whose vertices are (1,1), (2,4), (8,4) and (10,1). Justify the quadrilateral.

6. How will you describe the position of the table lamp on your study table to another person?

7. Draw the graph of y = 2x + 4. Use the graph to find the area between the line and the axes.

8. in which quadrant will the point lie, if:-
(a) ordinate is 3 and abscissa is – 7
(b) abscissa is – 10 and ordinate is – 4
(c) Ordinate is 4 and abscissa is – 6.

9. Fill in the blanks:-

(a) The coordinates of the origin 0 are ………………………

(b) The y coordinate of every point on the x-axis is ……………

(c) Distance along the x-axis is called ………………………

(d) Distance along the y-axis is called ………………………

(e) The point (x,y) = (y,x) only if ………………………