Question

Line A B has a negative slope and goes through points (negative m, p) and (w, z). Line A prime B prime has a positive slope and intersects with line A B.
Which coordinate for points A' and B' would help prove that lines AB and A'B' are perpendicular?

A': (p, m) and B': (z, w)
A': (p, m) and B': (z, −w)
A': (p, −m) and B': (z, w)
A': (p, −m) and B': (z, −w)

Answer 1

A': (p, m) and B': (z, −w)

Reason: slope(AB) = (z − p)/(w + m).
slope(A'B') = (−w − m)/(z − p) = −(w + m)/(z − p), which is the negative reciprocal of slope(AB). Their product is −1, so the lines are perpendicular.