# FRANK Solutions for Class 9 Maths Chapter 28 - Coordinate Geometry

Practise working with graphs by learning from TopperLearning’s Frank Solutions for ICSE Class 9 Mathematics Chapter 28 Coordinate Geometry. Revisit concepts like abscissa and ordinate by revising problems from your textbook along with the solutions by our experts. Also, understand how to draw graphs for equations given in a Maths problem.

You will find the Frank textbook solutions to be of great support if you struggle with Maths problems. With enough practice of these ICSE Class 9 Maths textbook solutions, you should be able to build your expertise in solving Maths questions. The reference answers will also guide you in reading graphs to extract information for finding answers.

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## Chapter 28 - Coordinate Geometry Exercise Ex. 28.1

Question 1

Find the value of 'a' and 'b' if

a. (a + 2,5 + b) = (1, 6)

b. (2a + b, a - 2b) = (7, 6)

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Plot the points O (0, 0), P (6, 0) and R (0, 5) on a graph. Find the coordinates of the point Q such that OPQR is a rectangle.

Solution 6

Q=(6,5)

Question 7

Plot the points A (3, 4) and C (-3, -2) on a graph. Find the coordinates of the point B and D such ABCD is a square. Also find the area of the square.

Solution 7

B=(-3,4)

D=(3,-2)

Question 8

Plot the points (-2, 3), (3, 3), (5, -2) and (-5, -2) on a graph and join them in order. Name the figure you get.

Solution 8

The quadrilateral obtained is a trapezium.

Question 9

Solution 9

Question 10(a)

In each of the following, find the coordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation.

Solution 10(a)

Question 10(b)

In each of the following, find the coordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation.

Solution 10(b)

Question 11

A rectangle PQRS is drawn on the coordinate axes such that P is the origin, PQ = 6 units and PS = 5 units. Find the coordinates of the vertices P, Q R and S. Also, find the area of the rectangle.

Solution 11

P=(0,0)

Q=(6,0)

R=(6,5)

S=(0,5)

## Chapter 28 - Coordinate Geometry Exercise Ex. 28.2

Question 1

Express the equation 3x + 5y + 15 = 0 in the form such that:

a. x is subject to the formula

b. y is dependent variable and x is independent variable.

Solution 1

Question 2

Draw a graph of each of the following equations:

a. x + 5 = 0

b. y - 4 = 0

c. 2x = 7

d. 2y - 5 = 0

e. x = 0

f. y = 3

Solution 2

Question 3

Draw a graph of each of the following equations:

a. x + 6y = 15

b. 3x - 2y = 6

c. 3y + 2x = 11

d. 5x + 2y = 16

e. x + y - 3 = 0

f. x = 3y

g.

h.

i.

j.

Solution 3

 x 9 3 -3 y 1 2 3

 x 2 4 -2 y 0 3 -6

 x 1 -2 -5 y 3 5 7

 x 2 4 6 y 3 -2 -7

 x 2 0 6 y 1 3 -3

 x -3 0 6 y 1 0 -2

 x 1 0 2 y 2.9 0.4 5.4

 x 2 -1 -2.5 y -1 -3 -4

 x 2 5 -1 y -7 1 -15

 x 5 -5 10 y 2 -4 5

Question 4

Solution 4

Question 5

Solution 5

Question 6

Draw a graph for each of the following equations and find the coordinates of the points where the line drawn meets the x-axis and y-axis:

a. 2x + 3y = 12

b.

Solution 6

 x 3 -3 6 y 2 6 0

 x 0 5 5/2 y 2 -2 0

Question 7

Solution 7

Question 8

Solution 8

Question 9

Draw the graph of the lines y = x + 2, y = 2x - 1 and y = 2 from x = -3 to 4, on the same graph paper. Check whether the lines drawn are parallel to each other.

Solution 9

 x 0 5 -3 y 2 7 -1

 x 0 -2 3 y -1 -5 5

The lines are not parallel to each other.

Question 10

Find the inclination and slope of a line which is

a. equidistant from the x-axis.

b. equidistant from the y-axis.

c. intersecting x-axis at right angle.

d. perpendicular to y-axis.

Solution 10

Question 11

Find the slope of the line whose inclination is given as

a.

b. 30°

c. 45°

d. 60°

Solution 11

Question 12

Find the inclination of the line whose slope is

a. 1

b.

Solution 12

Question 13

Find the slope and y-intercept for each of the following equations:

a. 3x - 8y + 24 = 0

b. 6x = 7y - 12

Solution 13

Question 14

Find the equation of the line, whose

a. slope is 3 and y-intercept is 5.

b. slope is 0 and y-intercept is -1.

c. slope is 1 and y-intercept is 0.

Solution 14

Question 15

Draw the graph of a line 2x + 3y = 6. From the graph, find the slope and y-intercept of the line.

Solution 15

 x 3 -3 0 y 0 4 2

Question 16

Draw the graph of the lines represented by the equations x + y = 4 and 2x - y = 2 on the same graph. Find the coordinates of the point where they intersect

Solution 16

 x 3 0 -1 y 1 4 5

 x 3 0 -1 y 4 -2 -4

 (2, 2)

Question 17

Draw the graph of the lines represented by the equations 3x - 2y = 4 and x + y = 3 on the same graph. Find the coordinates of the point where they intersect. State, whether the lines are perpendicular to each other.

Solution 17

Question 18

Solution 18

Question 19

Draw the graph of the lines represented by the equations 5y = 3x + 1 and y = 2x + 3 on the same graph. Find the coordinates of the point where they intersect.

Solution 19

 x -2 8 -7 y -1 5 -4

 x 0 -1 -7 y 3 1 -11

 (-2, -1)

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