F.4Maths

The eqaution of L1:
y-(-2) / x-0 = 0-(-2) / -3-0
y+2 /x = 2/-3
-3y-6=2x
y= (-2/3)x-2...(1)

The equation of L2:
y=mx
because L1 is perpendicular to L2.
so..
m*(-2/3)= -1
m=3/2

y=(3/2)x...(2)

sub (2) into (1),
(3/2)x=(-2/3)x-2
(13/6)x= -2
13x= -12
x= -12/13
sub x= -12/13 into (2),
y=(3/2)(-12/13)
y= -18/13

so,the coordinates of the intersection A is (-12/13 , -18/13).

The equation of L1 is x/(-3)+y/(-2)=1 and the slope is (-2-0)/(0+3)=-2/3
The equation of L2 is y=(3/2)x

Sub. y=(3/2)x into L1
x/(-3)+3x/(-4)=1
4x+9x=-12
x=-12/13
So y=-18/13

The coordinate of A is (-12/13,-18/13)