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
x01-1
y-3-5-1











(ii) $x-5 y-4=0 \Rightarrow x=5 y+4$

x4-1-6
y0-1-2











Question 2

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

Sol :
$3 y=12-2 x \quad \Rightarrow \quad y=\frac{12-2 x}{3}$
x036
y420










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

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

x61.20
y045










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-3-1.50
y024











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 

x012
y-4-12









(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.

x123a
y-2b4-5
Sol :
Draw the graph on graph paper and it is clear that from graph, b=1, a=0











Hence, a=0 , b=1

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