Question

$M$ is the midpoint of the straight line $PQ$. If $P(-2,9)$ and $M$ is $(4,3)$, find the coordinates of $Q$.

• A. $(1,6)$
• B. $(10,-3)$
• C. $(10,6)$
• D. $(8,-3)$

Answer 1

Answer: (B)

$(10,-3)$

Let the coordinates of point $Q$ be $(h,k).$

Now, by midpoint formulae,

$\begin{array}{cc}\left(\frac{h-2}{2},\frac{k+9}{2}\right)& =\left(4,3\right)\\ \frac{h-2}{2}=4\text{and}\frac{k+9}{2}& =3\\ h-2=8\text{and}k+9& =6\\ h=10\text{and}k& =-3\end{array}$

Hence, coordinates of point $Q$ is $(10,-3).$