**Co-ordinate Geometry Class-9 Concise** ICSE Maths Selina Solutions Chapter-26. We provide step by step Solutions of Exercise / lesson-26 **Co-ordinate Geometry** for ICSE **Class-9 Concise** Selina Mathematics by RK Bansal.

Our Solutions contain all type Questions with Exe-26 A, Exe-26 B, Exe-26 C to develop skill and confidence. Visit official Website **CISCE** for detail information about ICSE Board Class-9 Mathematics .

**Co-ordinate Geometry Class-9 Concise** ICSE Maths Selina Solutions Chapter-26

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**Exe-26 A, Co-ordinate Geometry Class-9 Concise ICSE Maths Selina Solutions **

**Question. 1 **

For the equation given below; name the dependent and independent variables

……………….

**Answer 1:**

**Question. 2 **

Plot the following points on the same graph paper:

(i) (8, 7)

(ii) (3, 6)

(iii) (0, 4)

(iv) (0, -4)

(v) (3, -2)

(vi) (-2, 5)

(vii) (-3, 0)

(viii) (5, 0)

(ix) (-4, -3)

**Answer 2:**

**
**On the graph paper, let us draw the co-ordinate axes XOX’ and YOY’ intersecting at the origin O. With proper scale, mark the numbers on the two co-ordinate axes.

Now for the point A(8,7)

Step I

Starting from origin O, move 8 units along the positive direction of X axis, to the right of the origin O

Step II

Now from there, move 7 units up and place a dot at the point reached. Label this point as A(8,7)

Similarly plotting the other points

**Question. 3 **

Find the values of x and y if:

(i). (x – 1, y + 3) = (4, 4)

(ii). (3x + 1, 2y – 7) = (9, – 9)

(iii). (5x – 3y, y – 3x) = (4, -4)

**Answer :3**

**Question. 4 **

Use the graph given alongside, to find the coordinates of the point (s) satisfying the given condition:

(i) The abscissa is 2.

(ii)The ordinate is 0.

(iii) The ordinate is 3.

(iv) The ordinate is -4.

(v) The abscissa is 5.

(vi) The abscissa is equal to the ordinate.

(vii) The ordinate is half of the abscissa.

**Answer :4**

(i) The abscissa is 2

Now using the given graph the co-ordinate of the given point A is given by (2,2)

(ii) The ordinate is 0

Now using the given graph the co-ordinate of the given point B is given by (5,0)

(iii) The ordinate is 3

Now using the given graph the co-ordinate of the given point C and E is given by (-4,3)& (6,3)

(iv) The ordinate is -4

Now using the given graph the co-ordinate of the given point D is given by (2,-4)

(v) The abscissa is 5

Now using the given graph the co-ordinate of the given point H, B and G is given by (5,5) ,(5,0) & (5,-3)

(vi)The abscissa is equal to the ordinate.

Now using the given graph the co-ordinate of the given point I,A & H is given by (4,4),(2,2) & (5,5)

(vii)The ordinate is half of the abscissa

Now using the given graph the co-ordinate of the given point E is given by (6,3)

**Question. 5**

State, true or false:

(i)The ordinate of a point is its x-co-ordinate.

(ii)The origin is in the first quadrant.

(iii)The y-axis is the vertical number line.

(iv)Every point is located in one of the four quadrants.

(v)If the ordinate of a point is equal to its abscissa; the point lies either in the first quadrant or in the second quadrant.

(vi)The origin (0,0) lies on the x-axis.

(vii)The point (a,b) lies on the y-axis if b=0.

**Answer 5:**

(i)The ordinate of a point is its x-co-ordinate.

False.

(ii)The origin is in the first quadrant.

False.

(iii)The y-axis is the vertical number line.

True.

(iv)Every point is located in one of the four quadrants.

True.

(v)If the ordinate of a point is equal to its abscissa; the point lies either in the first quadrant or in the second quadrant.

False.

(vi)The origin (0,0) lies on the x-axis.

True.

(vii)The point (a,b) lies on the y-axis if b=0.

False

**Question. 6**

In 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

(i) 3 – 2x = 7; 2y + 1 = 10 – 2 1/2y.

(ii)…………….

(iii)………………

**Answer 6:**

**Question. 7**

In the following, the coordinates of the three vertices of a rectangle ABCD are given. By plotting the given points; find, in case, the coordinates of the fourth vertex:

(i) A(2, 0), B(8, 0) and C(8, 4).

(ii)A (4, 2), B(-2, 2) and D(4, -2).

(iii) A (- 4, – 6), C(6, 0) and D(- 4, 0).

(iv).B (10, 4), C(0, 4) and D(0, -2).

**Answer 7:**

**
**After plotting the given points A(2,0), B(8,0) and C(8,4) on a graph paper; joining A with B and B with C. From the graph it is clear that the vertical distance between the points B(8,0) and C(8,4) is 4 units, therefore the vertical distance between the points A(2,0) and D must be 4 units. Now complete the rectangle ABCD

As is clear from the graph D(2,4)

(ii)A(4,2), B(-2,-2) and D(4,-2)

**After plotting the given points A(4,2), B(-2,2) and D(4,-2) on a graph paper; joining A with B and A with D. From the graph it is clear that the vertical distance between the points A(4,2) and D(4,-2) is 4 units and the horizontal distance between the points A(4,2) and B(-2,2) is 6 units , therefore the vertical distance between the points B(-2,2)and C must be 4 units and the horizontal distance between the points B(-2,2) and C must be 6 units. Now complete the rectangle ABCD**

As is clear from the graph C(-2,2)

**Question. 8**

A (- 2, 2), B(8, 2) and C(4, – 4) are the vertices of a parallelogram ABCD. By plotting the given points on a graph paper; find the co-ordinates of the fourth vertex D.

Also, form the same graph, state the co-ordinates of the mid-points of the sides AB and CD

**Answer 8:
**After plotting the given points A(2,-2), B(8,2) and C(4,-4) on a graph paper; joining B with C and B with A . Now complete the parallelogram ABCD.

As is clear from the graph D(-6,4)

Now from the graph we can find the mid points of the sides AB and CD.

Therefore the co-ordinates of the mid-point of AB is E(3,2) and the co-ordinates of the mid-point of CD is F(-1,-4)

**Question. 9**

A (-2, 4), C(4, 10) and D(-2, 10) are the vertices of a square ABCD. Use the graphical method to find the co-ordinates of the fourth vertex B. Also, find:

(i) The co-ordinates of the mid-point of BC;

(ii) The co-ordinates of the mid-point of CD and

(iii) The co-ordinates of the point of intersection of the diagonals of the square ABCD.

**Answer 9:**

**Question. 10**

By plotting the following points on the same graph paper. Check whether they are col linear or not:

(i) (3, 5), (1, 1) and (0, -1)

(ii) (-2, -1), (-1, -4) and (-4, 1)

**Answer 10:**

**Question. 11**

Plot point A(5, -7). From point A, draw AM perpendicular to the x-axis and AN perpendicular to the y-axis. Write the coordinates of points M and N

**Answer 11:**

**Question. 12**

In square ABCD; A = (3, 4), B = (-2, 4) and C = (-2, -1). By plotting these points on a graph paper, find the co-ordinates of vertex D. Also, find the area of the square

**Answer 12:**

**Question. 13**

In rectangle OABC; point O is the origin, OA = 10 units along x-axis and AB = 8 units. Find the co-ordinates of vertices A, B and C

**Answer 13:**

**Co-ordinate Geometry Exe-26 B, Class-9 Concise ICSE Maths Selina Solutions **

**Question 1:**

Draw the graph for each linear equation given below

(i) x = 3

(ii) x +3 =0

(iii) x -5 = 0

(iv) 2x-7 = 0

(v) y = 4

(vi) y + 6 = 0

(vii) y – 2 = 0

(viii) 3y + = 0

(ix) 2y – 5 = 0

(x) y = 0

(xi) x = 0

**Answer 1**

**Question 2:**

Draw the graph for each linear equation given below

(i) y = 3x

(ii) y = -x

(iii) y = – 2x

(iv) y = x

(v) 5x + y = 0

(vi) x + 2y = 0

(vii) 4x -y = 0

(viii) 3x + 2y = 0

(ix) x = – 2y

**Answer 2**

**Question 3:**

Draw the graph for each linear equation given below

(i) y = 2x + 3

(ii) y = 2x /3 -1

(iii) y = – x + 4

(iv) y = 4x – 5/2

(v) y = 3x/2 + 2/3

(vi) 2x – 3y = 4

(vii) …………..

(viii) ……………..

(ix) ……………..

**Answer 3**

**Question 4:**

Draw the graph for each linear equation given below

(i) 3x + 2y =6

(ii) 2x – 5y =10

(iii) x/2 + 2y/3 = 5

(iv) ………………..

**Answer 4**

**Question 5:**

For the linear equation, given above, draw the graph and then use the graph drawn (in the following case) to find the area of a triangle enclosed by the graph and the co-ordinates axes:

(i) 3x – (5 – y) = 7

(ii) 7 – 3 (1 – y) = – 5 + 2x.

**Answer 5**

**Question 6:**

For the pair of linear equations given below, draw graphs and then state, whether the lines drawn are parallel or perpendicular to each other

(i) y = 3x – 1 , y = 3x + 2

(ii) y = x – 3 , y = – x + 5

(iii) 2x – 3y = 6 , x/2 + y/3 =1

(iv) 3x + 4y = 24, x/4 + y/3 = 1

**Answer 6**

**Question 7:**

On the same graph paper, plot the graph of y = x – 2, y = 2x + 1 and y = 4 from x= – 4 to 3.

**Answer 7**

**Question 8:**

On the same graph paper, plot the graphs of y = 2x – 1, y = 2x and y = 2x + 1 from x = – 2 to x = 4. Are the graphs (lines) drawn parallel to each other?

**Answer 8**

**Question 9:**

The graph of 3x + 2y = 6 meets the x=axis at point P and the y-axis at point Q. Use the graphical method to find the co-ordinates of points P and Q.

**Answer 9**

**Question 10:**

Draw the graph of equation x + 2y – 3 = 0. From the graph, find:

(i) x_{1}, the value of x, when y = 3

(ii) x_{2}, the value of x, when y = – 2.

**Answer 10**

**Question 11:**

Draw the graph of the equation 3x – 4y = 12.

Use the graph drawn to find:

(i) y_{1}, the value of y, when x = 4.

(ii) y_{2}, the value of y, when x = 0.

**Answer 11**

**Question 12:**

Draw the graph of equation x/4+y/5=1 Use the graph drawn to find:

(i) x_{1}, the value of x, when y = 10

(ii) y_{1}, the value of y, when x = 8.

**Answer 12**

**Question 13:**

Use the graphical method to show that the straight lines given by the equations x + y = 2, x – 2y = 5 and x3+y=0 pass through the same point.

**Answer 13**

**Exe-26 C, Co-ordinate Geometry Class-9 Concise ICSE Maths Selina Solutions **

**Question 1:**

In each of the following, find the inclination of line AB

(i)…………….

(ii) …………………

(iii) ……………..

**Answer 1**

The angle which a straight line makes with the positive direction of x-axis (measured in anticlockwise direction) is called inclination o the line.

The inclination of a line is usually denoted by θ

(i)The inclination is θ = 45°

(ii) The inclination is θ = 135°

(iii) The inclination is θ = 30°

**Question 2:**

Write the inclination of a line which is:

(i) Parallel to the x-axis

(ii) Perpendicular to the x-axis

(iii)Parallel to the y-axis.

(iv) Perpendicular to the y-axis.

**Answer 2**

(i)The inclination of a line parallel to x-axis is θ = 0°

(ii)The inclination of a line perpendicular to x-axis is θ = 90°

(iii) The inclination of a line parallel to y-axis is θ = 90°

(iv) The inclination of a line perpendicular to y-axis is θ = 0°

**Question 3:**

Write the slope of the line whose inclination is:

(i) 0

(ii) 30

(iii) 45

(iv) 60

**Answer 3**

**Question 4:**

Find the inclination of the line whose slope is

(i) 0

(ii) 1

(iii) √3

(iv) 1/√3

**Answer 4**

**Question 5:**

Write the slope of the line which is

(i) Parallel to the x-axis

(ii) Perpendicular to the x-axis.

(iii) Parallel to the y-axis.

(iv) Perpendicular to the y-axis.

**Answer 5**

**Question 6:**

For the equation given below, find the slope and the y-intercept:

(i) x + 3y + 5 = 0

(ii) 3x – y – 8 = 0

(iii) 5x = 4y + 7

(iv) x= 5y – 4.

(v) y = 7x – 2

(vi) 3y = 7

(vii) 4y + 9 = 0

**Answer 6**

**Question 7:**

Find the equation of the line whose:

(i) Slope = 2 and y-intercept = 3

(ii) Slope = 5 and y-intercept = – 8

(iii) slope = – 4 and y-intercept = 2

(iv) slope = – 3 and y-intercept = – 1

(v) slope = 0 and y-intercept = – 5

(vi) slope = 0 and y-intercept = 0

**Answer 7**

**Question 8:**

Draw the line 3x + 4y = 12 on a graph paper. From the graph paper, read the y-intercept of the line

**Answer 8**

Given line is 3x + 4y = 12

The graph of the given line is shown below.

Clearly from the graph we can find the y-intercept.

The required y-intercept is 3.

**Question 9:**

Draw the line 2x – 3y – 18 = 0 on a graph paper. From the graph paper, read the y-intercept of the line.

**Answer 9**

Given line is

2x – 3y – 18 = 0

The graph of the given line is shown below.

Clearly from the graph we can find the y-intercept.

The required y-intercept is -6

**Question 10:**

Draw the graph of the line x + y = 5. Use the graph paper drawn to find the inclination and the y-intercept of the line.

**Answer 10**

Given line is

x + y = 5

The graph of the given line is shown below.

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