Answer:
(B)A': (p, m) and B': (z, −w)
Step-by-step explanation:
Line AB has a negative slope and goes through points (-m, p) and (w, z).
Line A'B' has a positive slope and intersects with line AB.
Definition: Two lines are perpendicular if the product of their slopes is -1.
Slope of AB
[tex]m_1=\dfrac{z-p}{w-(-m)} \\m_1=\dfrac{z-p}{w+m}[/tex]
From the options, we consider the coordinates whole slope multiplied by the slope of AB gives a result of -1.
In Option B: A': (p, m) and B': (z, −w)
Slope of A'B'
[tex]m_2=\dfrac{-w-m}{z-p} \\m_2=\dfrac{-(w+m)}{z-p}[/tex]
The product of the slopes
[tex]m_1m_2=\dfrac{z-p}{w+m}\times \dfrac{-(w+m)}{z-p} =-1[/tex]
Therefore, the coordinate for points A' and B' which would help prove that lines AB and A'B' are perpendicular is A': (p, m) and B': (z, −w).
You can try to calculate the slope of the others. They would not satisfy this condition.
