答案:(a) $A’=(-4-3)$, $B’=(9,9)$
- $A’ = (-4,-3)$,$B’ = (9,9)$。
- 考慮 $AB$ 的斜率,可得
$\begin{array}{rcl}
m_{AB} & = & \dfrac{-9 -4}{9 – (-3)} \\
& = & \dfrac{-13}{12}
\end{array}$考慮 $A’B’$ 的斜率,可得
$\begin{array}{rcl}
m_{A’B’} & = & \dfrac{9 -(-3)}{9-(-4)} \\
& = & \dfrac{12}{13}
\end{array}$由此,可得
$\begin{array}{rcl}
m_{AB} \times m_{A’B’} & = & \dfrac{-13}{12} \times \dfrac{12}{13} \\
& = & -1
\end{array}$所以,$AB$ 與 $A’B’$ 互相垂直。