Question

Use graph paper for this question. Take 2 cm=1 unit on both the axes,
(i) Draw the graphs of x+y+3=0 and 3x-2y+4=0. Plot only three points per line.
(ii) Write down the co-ordinates of the point of intersection of the lines.
(iii) Measure and record the distance of the point of intersection of the lines from the origin in cm.

Answer 1

(i) $x+y+3=0$ …(i)
$y=-x-3$
When $x=-3$
$y=3-3=0$
when $x=-2$
$y=2-3=-1$
when $x=-1$
$y=1-3=-2$

$x$	$=-1$,	$,-2$	$,-3$
$y$	$=-2,$	$,-1$	$,0$

Mark the above points on graph. Join them.
$3x-2y+4=0$ …(ii)
$2y=3x+4$
$y=(3x+4)/2$
When $x=-4$
$y=(3\times -4+4)/2=(-12+4)/2=-8/2=-4$
When $x=-2$
$y=(3\times -2+4)/2=(-6+4)/2=-2/2=-1$
When $x=2$
$y=(3\times 2+4)/2=(6+4)/2=10/2=5$

$x=$	$-4$	$,-2$	$,2$
$y=$	$-4$	$,-1$	$,5$

Mark the above points on graph. Join them.
(ii)The two lines intersect at $(-2,-1).$
(iii)Measure the distance from origin to the point $(-2,-1).$
The distance of the point of intersection of the lines from the origin is $4.5$ cm