Line CD contains the points (-4,1), (-1,5) and (5, 13). if AB _I_ CD, A(2,2) and B (-4,k),what is the value of k? write answer as a reduced fraction

Answer 1

I assume the question states that A is perpendicular to B. In that case, if y = mx + b and y' is the perpendicular function, then y' = -1/m*(x) + b.

Notice that line CD has a positive slope since y increases as x increases.....Here,

m_cd = (y_max y_min)cd/(x_max - x_min)_cd = (13-1)/(5-(-4)) = 12/9 = 4/3.

Therefore, the perpendicular slope, m' = -1/m = -1/(4/3)) = -3/4.

Because y decreases as x increases, we have

m' = -3/4 = (y_min - y_max)_AB/(x_max-x_min)_AB = (2-k)/(2- (-4))

=(2-k)/(6)--> (2-k) = 6*(-3/4) = -18/4 --> k = 8/4 + 18/4 = 26/4 or 13/2.

Answer 2

We can calculate the slope of line CD using any two of the three points:

m = (y2 - y1)/(x2 - x1) = (5 - 1)/(-1 + 4) = 4/3

Perpendicular lines have opposite reciprocal slopes, so line AB should have a slope of -3/4.

Using the slope formula again with points A and B:

-3/4 = (k - 2)/(-4 - 2)

-3/4 = (k - 2)/(-6) multiply both sides by -6

9/2 = k - 2 add 2 to both sides

k = 13/2 = 4.5

Hope this helps!