three points have the coordinates A(2,9) B(4,3) and C(2,-5). The line through C with gradient 0.5 meets the line AB produced at D. Calculate the coordinates of D.

Answer 1

Using the two-point form of the line, line AB is

y-9 = (3-9)/(4-2) * (x-2)
y = -3x + 15

Using the point-slope form of the line, line CD is

y-(-5) = .5 (x-2)
y = .5x - 6

So, point D is where the two lines intersect:

-3x + 15 = .5x - 6
21 = 3.5x
x = 6

Since CD has slope .5, y increases by .5 when x increases by 1. Since x=6 is 4 units to the right, we want y 2 more than -5 = -3

So, D = (6,-3)