ML Aggarwal Solution Class 9 Chapter 19 Coordinate Geometry Exercise 19.2

 Exercise 19.2

Question 1

Draw the graphs of the following linear equations :

(i) 2x + + 3 = 0

(ii) x- 5y- 4 = 0

Sol :

(i) 2x+y+3=0⇒y=-2x-3

x	0	1	-1
y	-3	-5	-1

(ii) $x-5 y-4=0 \Rightarrow x=5 y+4$

x	4	-1	-6
y	0	-1	-2

Question 2

Draw the graph of 3y= 12 – 2x. Take 2cm = 1 unit on both axes.

Sol :

$3 y=12-2 x \quad \Rightarrow \quad y=\frac{12-2 x}{3}$

x	0	3	6
y	4	2	0

Question 3

Draw the graph of 5x + 6y – 30 = 0 and use it to find the area of the triangle formed by the line and the co-ordinate axes.

Sol :

$5 x+6 y-30=0  \Rightarrow 5 x+6 y=30$

$\Rightarrow 5 x=30-6 y \Rightarrow \quad x=\frac{30-6 y}{5}$

x	6	1.2	0
y	0	4	5

Area of triangle formed by the line and coordinate axes

$=\frac{1}{2} \times \mathrm{OA} \times \mathrm{OB}=\frac{1}{2} \times 6 \times 5=3 \times 5=15$ sq. units

Question 4

Draw the graph of 4x- 3y + 12 = 0 and use it to find the area of the triangle formd by the line and the co-ordinate axes. Take 2 cm = 1 unit on both axes.

Sol :

4x-3y+12=0

$\Rightarrow  4 x=3 y-12 \Rightarrow x=\frac{3 y-12}{4}$

When y=0 ,$x=\frac{3 \times 0-12}{4}=\frac{0-12}{4}=\frac{-12}{4}=-3$

y=2 , $x=\frac{3 \times 2-12}{4}=\frac{6-12}{4}=\frac{-6}{4}=-1.5$

y=4 , $x=\frac{3 \times 4-12}{4}=\frac{12-12}{4}=\frac{0}{4}=0$

Table of value 

x	-3	-1.5	0
y	0	2	4

Area of the triangle formed by the line and the coordinates axes 

$=\frac{1}{2} \times|\mathrm{OA}| \times|\mathrm{OB}|$

$=\frac{1}{2} \times 3 \times 4=\frac{1}{2} \times 4 \times 3=2 \times 3=6$ sq. units

Question 5

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

(i) the value of y when x = -1

(ii) the value of x when y = 5.

Sol :

y=3x-4 , when x=0 , y=3×0-4=0-4=-4

$x=1, y=3 \times 1-4=3-4=-1$

$x=2, y=3 \times 2-=6-4=2$

Table of value 

x	0	1	2
y	-4	-1	2

(i) The value of y=-7, when x=-1

(ii) The value of x=3, when y=5.

Question 6

The graph of a linear equation in x and y passes through (4, 0) and (0, 3). Find the value of k if the graph passes through (A, 1.5).

Sol :

Plot the points A(4,0) and B(0,3) on the graph paper. From graph it is clear that k=2

Question 7

Use the table given alongside to draw the graph of a straight line. Find, graphically the values of a and b.

x	1	2	3	a
y	-2	b	4	-5

Sol :

Draw the graph on graph paper and it is clear that from graph, b=1, a=0

Hence, a=0 , b=1