Chapter 28 : Coordinate Geometry - Frank Solutions for Class 9 Maths ICSE

Mathematics in ICSE Class 9 is one of the most challenging and trickiest subjects of all. It includes complex topics such as logarithms, expansions, indices and Pythagoras Theorem which are difficult to understand for an average student. TopperLearning provides study materials for ICSE Class 9 Mathematics to make the subject easy and help students to clear all their concepts. Our study materials comprise numerous video lessons, question banks, revision notes and sample papers which help achieve success in the examination.

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Chapter 28 - Coordinate Geometry Excercise 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

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

  

Question 11

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 11

  

Question 12

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 12

 

  

 

P=(0,0)

Q=(6,0)

R=(6,5)

S=(0,5)

 

  

Chapter 28 - Coordinate Geometry Excercise 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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