Q1) "▲LMN has vertices L(-1,2) and M(-4,-1).

a) Find the coordinates of N such that ▲LMN is a right triangle.

b) Is there more than one solution? Explain."

So, basically, it's telling me to find the coordinates of N, and that one of the angles is 90 degrees/perpendicular.

a)

sketching a graph of LM will make it easier to solve.

N = (-1, -1) or (-4, 2)

angle LNM = 90 degrees.

b)

There are actually infinite number of solutions....answers in a) assumed that angle LNM is the right angle.

however, if now either angles LMN or MLN are assumed right angles, the coordinates of N cannot be determined.