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

Answer:

B. A': (p, m) and B': (z, −w)

Step-by-step explanation:

Answer 2

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

$m_1=\dfrac{z-p}{w-(-m)} \\m_1=\dfrac{z-p}{w+m}$

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'

$m_2=\dfrac{-w-m}{z-p} \\m_2=\dfrac{-(w+m)}{z-p}$

The product of the slopes

$m_1m_2=\dfrac{z-p}{w+m}\times \dfrac{-(w+m)}{z-p} =-1$

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.