Answer:
b
Step-by-step explanation:
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For AB and A'B' to be perpendicular, then the coordinates of A'B' is A': (p, m) and B': (z, −w)
Given that the coordinates of AB is at A(-m, p) and B(w, z). The slope of the line AB is given by:
[tex]slope\ of\ AB=\frac{y_2-y_1}{x_2-x_1}=\frac{z-p}{w-(-m)} =\frac{z-p}{w+m}[/tex]
Two lines are perpendicular if the product of their slopes is -1. Hence the slope of A'B' is:
slope of A'B' × slope of AB = -1
(z-p)/(w+m) × slope of A'B' = -1
slope of A'B' = (-w-m)/(z-p)
A) A': (p, m) and B': (z, w)
slope of A'B' = (w-m)/(z-p)
Option A is wrong
B) A': (p, m) and B': (z, -w)
slope of A'B' = (-w-m)/(z-p)
Option B is correct
C) A': (p, -m) and B': (z, w)
slope of A'B' = (w+m)/(z-p)
Option C is wrong
D) A': (p, -m) and B': (z, -w)
slope of A'B' = (-w+m)/(z-p)
Option is D wrong
Therefore for AB and A'B' to be perpendicular, then the coordinates of A'B' is A': (p, m) and B': (z, −w)
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