Ans: (a) $(-5,1)$ (b) Yes
- Note that the coordinates of $B$ are $(-6,-4)$. Then we have
$\begin{array}{rcl}
M & = & \left( \dfrac{-4+(-6)}{2} , \dfrac{6+(-4)}{2} \right) \\
& = & (-5, 1)
\end{array}$ - Slope of $OM$
$\begin{array}{cl}
= & \dfrac{1-0}{-5-0} \\
= & \dfrac{-1}{5}
\end{array}$Slope of $AB$
$\begin{array}{cl}
= & \dfrac{-4-6}{-6-(-4)} \\
= & 5
\end{array}$Since slope of $AB$ $\times$ slope of $OM$ $=-1$, then $OM$ is perpendicular to $AB$.
