##### Co-ordinate Geometry Class 9th Mathematics Part Ii MHB Solution

**Practice Set 7.1**

- State in which quadrant or on which axis do the following points lie. A(-3, 2), B(-5,…
- In which quadrant are the following points? i. whose both co-ordinates are positive.…
- Draw the co-ordinate system on a plane and plot the following points. L(-2, 4), M(5,…

**Practice Set 7.2**

- On a graph paper plot the points A (3,0), B(3,3), C(0,3). Join A, B and B, C. What is…
- Write the equation of the line parallel to the Y-axis at a distance of 7 units from it…
- Write the equation of the line parallel to the X-axis at a distance of 5 units from it…
- The point Q(-3, -2) lies on a line parallel to the Y-axis. Write the equation of the…
- Y-axis and line x = -4 are parallel lines. What is the distance between them?…
- Which of the equations given below have graphs parallel to the X-axis, and which ones…
- On a graph paper, plot the points A(2, 3), B(6, -1) and C(0, 5). If those points are…
- Draw the graphs of the following equations on the same system of co-ordinates. Write…
- x + y = 2 Draw the graphs of the equations given below
- 3x-y = 0 Draw the graphs of the equations given below
- 3x-y = 0 Draw the graphs of the equations given below

**Problem Set 7**

- What is the form of co-ordinates of a point on the X-axis? Choose the correct…
- Any point on the line y=x is of the form ..... Choose the correct alternative answer…
- What is the equation of the X-axis? Choose the correct alternative answer for the…
- In which quadrant does the point (-4, -3) lie? Choose the correct alternative answer…
- What is the nature of the line which includes the points (-5,5), (6,5), (-3,5), (0,5)?…
- Which of the points P (-1,1), Q (3,-4), R(1,-1), S (-2,-3), T (-4,4) lie in the fourth…
- Some points are shown in the figure 7.11 With the help of it answer the following…
- Without plotting the points on a graph, state in which quadrant or on which axis do the…
- Plot the following points on the one and the same co-ordinate system. A(1, 3), B(-3,…
- In the graph alongside, line LM is parallel to the Y-axis. (Fig. 7.12) i. What is the…
- How many lines are there which are parallel to X-axis and having a distance 5 units?…
- If ‘a’ is a real number, what is the distance between the Y-axis and the line x = a?…

###### Practice Set 7.1

**Question 1.**

State in which quadrant or on which axis do the following points lie.

A(-3, 2), B(-5, -2), K(3.5, 1.5),

D(2, 10), E(37, 35), F(15, -18),

G(3, -7), H(0, -5), M(12, 0),

N(0, 9), P(0, 2.5), Q(-7, -3)

**Answer:**

The x-y coordinate system is shown below:

The points are calculated as below:

**Question 2.**

In which quadrant are the following points?

i. whose both co-ordinates are positive.

ii. whose both co-ordinates are negative.

iii. whose x co-ordinate is positive, and the y co-ordinate is negative.

iv. whose x co-ordinate is negative and y co-ordinate is positive.

**Answer:**

According to co-ordinates Geometry,

i. In First Quadrant, both co-ordinates are positive.

ii.In Third Quadrant, both co-ordinates are negative.

iii.In Fourth Quadrant, x co-ordinate is positive and the y co-ordinate is negative.

iv.In second Quadrant, x co-ordinate is negative and y co-ordinate is positive.

The coordinate-system is shown below:

**Question 3.**

Draw the co-ordinate system on a plane and plot the following points.

L(-2, 4), M(5, 6), N(-3, -4), P(2, -3), Q(6, -5), S(7, 0), T(0, -5)

**Answer:**

The graph is shown below:

__Steps for plotting the points:__

• Draw X-axis and Y-axis on the plane.

• To find the point M(5,6) draw a line parallel to the Y-axis through the point on X axis which represents the number 5. Through the point on Y-axis which represents the number 6 draw a line parallel to the X-axis .

• The point of intersection of these two lines parallel to the Y and X-axis respectively, is the point M(5,6).

• In the same way, plot the point Q (6,-5),P(2,-3),L(-2,4) and N(-3,-4).

• and the point S(7,0) is lies on X-axis and the point T(0,-5) lies on Y-axis.

###### Practice Set 7.2

**Question 1.**

On a graph paper plot the points A (3,0), B(3,3), C(0,3). Join A, B and B, C. What is the figure formed?

**Answer:**

The graph is shown below:

__Steps are given below:__

• O is a centre of XY planes.

• Firstly we have drawn a point A(3,0) which is lies on x-axis and then,

• To find the point B(3,3) draw a line parallel to the Y-axis through the point on X axis which represents the number 3. Through the point on Y-axis which represents the number 3 draw a line parallel to the X-axis .

• And then draw a point C(0,3) is lies on y-axis and,

• Joining a points A,B,C and O then it is formed a SQUARE.

**Question 2.**

Write the equation of the line parallel to the Y-axis at a distance of 7 units from it to its left.

**Answer:**

The equation of line parallel to Y-axis is x = a

a = -7 (because 7 units from left)

x = -7 is required equation.

X-Values

__Steps to draw:__

• On a graph paper draw the X-axis and the Y-axis.

• Since it is given that x = -7, draw a line on the left of the Y-axis at a distance of 7 units from it and parallel to it.

**Question 3.**

Write the equation of the line parallel to the X-axis at a distance of 5 units from it and below the X-axis.

**Answer:**

The equation of line parallel to X-axis is y = a

a = -5 (because 5 units below the x-axis)

y = -5 is required equation.

__Steps:__

• On a graph paper draw the X-axis and the Y-axis.

• Since it is given that y = -5, draw a line below the X-axis at a distance of 5 units from it and parallel to it.

**Question 4.**

The point Q( -3, -2) lies on a line parallel to the Y-axis. Write the equation of the line and draw its graph.

**Answer:**

The equation of line parallel to y-axis is x = a

x = -3

And the given point is Q(-3,-2)

**Question 5.**

Y-axis and line x = -4 are parallel lines. What is the distance between them?

**Answer:**

The equation of line parallel to Y-axis is x = a.

x = -4

a = -4

Since the distance between and the line is 4 units.

The graph is shown below:

**Question 6.**

Which of the equations given below have graphs parallel to the X-axis, and which ones have graphs parallel to the Y-axis?

i. x=3 ii. y – 2 = 0

iii. x + 6 = 0 iv. Y = -5

**Answer:**

i. x = 3

x = a

The line is parallel to y-axis.

The figure is shown below:

ii. y-2 = 0

y = 2

y = a

The figure is shown below:

And the line is parallel to x-axis.

iii. x + 6 = 0

x = -6

The figure is shown below:

And the line is parallel to y-axis.

iv. y = -5

y = a

Then, the line is parallel to x-axis.

The figure is shown below:

**Question 7.**

On a graph paper, plot the points A(2, 3), B(6, -1) and C(0, 5). If those points are collinear then draw the line which includes them. Write the co-ordinates of the points at which the line intersects the X-axis and the Y-axis.

**Answer:**

The figure is shown below:

• Yes, given points are collinear.

• The line intersects the x-axis at point D(5,0) and the y-axis at point C(0,5).

**Question 8.**

Draw the graphs of the following equations on the same system of co-ordinates. Write the co-ordinates of their points of intersection.

x + 4 = 0

y - 1 = 0

2x + 3 = 0

3y - 15 = 0

**Answer:**

Given equation are

The figure is shown below:

• On a graph paper draw the X-axis and the Y-axis.

• Since it is given that x = -4 and x = -1.5, draw a line on the left of the Y-axis at a distance of 4 and 1.5 units from it and parallel to it.

• Since it is given that y = 1 and y = 5, draw a line above the X-axis at a distance of 1and 5 units from it and parallel to it.

• These lines, parallel to the two axes, are the graphs of the given equations.

• And these lines are intersects at the point A(-1.5,1), B(-4,1),C(-1.5,5) and D(-4,5).

**Question 9.**

Draw the graphs of the equations given below

x + y = 2

**Answer:**

x + y = 2

According to the equation,

• Firstly we have findout the point with the help of given equation.

• Then after plot a xy plane in a coordinate axis.

• The points A,B and C are collinear because all the points lies in the straight line.

**Question 10.**

Draw the graphs of the equations given below

3x-y = 0

**Answer:**

3x-y = 0

According to the given equation,

Now we have find out the points are

• On a graph paper draw the X-axis and the Y-axis.

• Then the points A,B and c are collinear because its lies in a straight line.

**Question 11.**

Draw the graphs of the equations given below

3x-y = 0

**Answer:**

2x + y = 1

According to the given equation,

Now we have find out the points are

• On a graph paper draw the X-axis and the Y-axis.

• Then the points A,B and c are collinear because its lies in a straight line.

###### Problem Set 7

**Question 1.**

Choose the correct alternative answer for the following questions.

What is the form of co-ordinates of a point on the X-axis?

A. (b,b)

B. (o,b)

C. (a,o)

D. (a,a)

**Answer:**

This is because the y co-ordinate point is zero.

**Question 2.**

Choose the correct alternative answer for the following questions.

Any point on the line y=x is of the form .....

A. (a,a)

B. (o,a)

C. (a,o)

D. (a,-a)

**Answer:**

y = x

Y = a then x = a.

**Question 3.**

Choose the correct alternative answer for the following questions.

What is the equation of the X-axis?

A. x =0

B. y =0

C. x+y=0

D. x=y

**Answer:**

y = m × x + c

Where c is the intercept of the line on y-axis and m is the gradient of the line. Since intercept of x-axis on y-axis is zero, so c = 0. Gradient of x-axis is also zero because it makes an angle zero with itself. So m = tan(theta) = 0. Putting these values in the general equation we get,

y = 0 × x + 0

y = 0. Thus we get the equation for x-axis as y = 0.

**Question 4.**

Choose the correct alternative answer for the following questions.

In which quadrant does the point

(-4, -3) lie?

A. First

B. Second

C. Third

D. Fourth

**Answer:**

Since both the x & y coordinate are negative. Hence, it lies in the third quadrant.

**Question 5.**

Choose the correct alternative answer for the following questions.

What is the nature of the line which includes the points (-5,5), (6,5),

(-3,5), (0,5)?

A. Passes through the origin,

B. Parallel to Y-axis.

C. Parallel to X-axis

D. None of these

**Answer:**

All the points are shown below:

**Question 6.**

Choose the correct alternative answer for the following questions.

Which of the points P (-1,1), Q (3,-4), R(1,-1), S (-2,-3), T (-4,4) lie in the fourth quadrant?

A. P and T

B. Q and R

C. only S

D. P and R

**Answer:**

For a point to lie in the 4^{th} quadrant, the x-coordinate should be positive & the y-coordinate should be negative.

As shown in the figure:

The figure is given below:

**Question 7.**

Some points are shown in the figure 7.11

With the help of it answer the following questions :

i. Write the co-ordinates of the points Q and R.

ii. Write the co-ordinates of the points T and M.

iii. Which point lies in the third quadrant?

iv. Which are the points whose x and y co-ordinates are equal?

**Answer:**

i. The co-ordinates of the points are Q(-2,2) and R(4,-1).

ii. The co-ordinates of the points are T(0,-1) and M(3,0).

iii. The point lies in the third quadrant is S(-3,-2).

iv. Q(-2,2) (both the co-ordinates are equal)

**Question 8.**

Without plotting the points on a graph, state in which quadrant or on which axis do the following point lie.

i. (5, -3) ii. (-7, -12)

iii. (-23, 4) iv. (-9, 5)

v. (0, -3) vi. (-6, 0)

**Answer:**

We should plot the points according to the coordinate system:

**Question 9.**

Plot the following points on the one and the same co-ordinate system.

A(1, 3), B(-3, -1), C(1, -4),

D(-2, 3), E(0, -8), F(1, 0)

**Answer:**

We plot according to the coordinate system:

**Question 10.**

In the graph alongside, line LM is parallel to the Y-axis. (Fig. 7.12)

i. What is the distance of line LM from the Y-axis?

ii. Write the co-ordinates of the points P, Q and R.

iii. What is the difference between the x co-ordinates of the points L and M?

**Answer:**

i.The distance of line LM from the Y-axis is 3.

ii.The co-ordinates of the points are P(3,2),Q(3,-1)and R(3,0).

iii. The difference between the x co-ordinates of the points L and M is 6.

**Question 11.**

How many lines are there which are parallel to X-axis and having a distance 5 units?

**Answer:**

Suppose the required linear equation of a line is y = mx + c

Since, the line is parallel to x-axis, so m = 0

Then equation of the line will be y = c

And this line passes through the point at a distance of 5 units below the x-axis i.e (-5,0)

Then the equation of line is y = -5.

And similarly,

And this line passes through the point at a distance of 5 units above the x-axis i.e (5,0)

Then the equation of line is y = 5.

**Question 12.**

If ‘a’ is a real number, what is the distance between the Y-axis and the line x = a?

**Answer:**

The distance is *a* unit, assuming *a* is an arbitrary constant, which it is, given that you stated it’s a real number.

This is because the y-axis is the same as the line *x* = 0, and so the difference between the two lines will be *a*−0 units, or simply *a* units.