Question

Line L1 has equation 2x -3y+12=0
Gradient of L1 is 2/3x

The line L1 crosses the x axis at the point A and the y axis at the point B.

The line L2 is perpendicular to L1 and passes through B.

A) find and equation of L2

The line L2 crosses the x axis at the point C

B) find the area of triangle ABC

Thankyou

Answer 1

L1 has intercepts at A:(-6,0) and B:(0,4)
L2 has gradient -3/2 and passes through (0,4), so L2 is

y-4 = (-3/2)(x-0)
3x+2y-8 = 0
L2 passes through B:(0,4) and C:(8/3,0)

So, if you plot the points, you can see that you have a triangle with base along the x-axis, and its third point on the y-axis.