Question

given: $overleftrightarrow{pq} perp overleftrightarrow{pq}$
prove: $left( m_{overleftrightarrow{pq}}
ight) left( m_{overleftrightarrow{pq}}
ight) = -1$

1. $m_{overleftrightarrow{pq}} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{clubsuit}{c - a}$ $clubsuit = d - b$
2. $m_{overleftrightarrow{pq}} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{c - a}{heartsuit}$ $heartsuit = -d - (-b)$
3. $m_{overleftrightarrow{pq}} = \frac{c - a}{-d - (-b)} = \frac{c - a}{spadesuit}$ $spadesuit =$ dropdown options: $d - b$, $-d + b$, $-d - b$

check

graph: coordinate plane with points $p(a, b)$, $p(-b, a)$, $q(c, d)$, $q(-d, c)$

Explanation:

Step1: Simplify the denominator

We have the denominator \(-d - (-b)\). Using the rule of subtracting a negative (which is equivalent to adding the positive), we get \(-d + b\). So we simplify \(\frac{c - a}{-d - (-b)}\) to \(\frac{c - a}{-d + b}\).

Answer:

\(-d + b\)