Question

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

Answer:

b

Step-by-step explanation:

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Answer 2

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:

$slope\ of\ AB=\frac{y_2-y_1}{x_2-x_1}=\frac{z-p}{w-(-m)} =\frac{z-p}{w+m}$

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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