this one is killing me for some reason:

Question

Find any of the values of k so that
(-3, 4), (-8,5), and (-5, k) are the verticles of a right traingle.

Answer 1

To have a right angle, the lines must meet perpendicular.
To have perpendicular lines their slopes must be opposite reciprocals of each other.

From a rough sketch it looks like the right angle could be at (-5,k), so

(k-5)/(-5+8) = -(-5+3)/(k-4)
(k-5)/3 = 2/(k-4)
k^2 - 9k + 20 = 6
k^2 - 9k + 14 = 0
(k-2)(k-7) = 0
k = 2 or k = 7

make a sketch to illustrate that both values of k are valid.

BTW, verticles ?, I call them verices.

Answer 2

you rock Reiny! And BTW..I call them vertices also...it was a typo.

Thanks for your help!