Find the endpoint, Q, given $\mathit{P}\mathbf{ }\mathbf{(}\mathbf{–}\mathbf{7}\mathbf{,}\mathbf{ }\mathbf{–}\mathbf{9}\mathbf{.}\mathbf{4}\mathbf{)}$ and midpoint $\mathit{M} \mathbf{(}\mathbf{–}\mathbf{10}\mathbf{,}\mathbf{ }\mathbf{–}\mathbf{3}\mathbf{.}\mathbf{55}\mathbf{)}$. Then show your answer is correct using the midpoint formula.

Find Q

$$\begin{gathered} P \left(–7, –9.4\right), M \left(–10, –3.55\right) \\ \left(\frac{x+–7}{2}, \frac{y+–9.4}{2}\right)=\left(–10, –3.55\right) \\ \begin{array}{ccc}\frac{x+–7}{2}=–10& & \frac{y–9.4}{2}=–3.55\\ x–7=–20& & y–9.4=–7.1\\ x=–13& & y=2.3\\ & Q \left(–13, 2.3\right)& \end{array} \end{gathered}$$

Check M is the midpoint between P and Q

$$\begin{gathered} P \left(–7, –9.4\right), M \left(–10, –3.55\right), Q \left(–13, 2.3\right) \\ \left(\frac{–13+–7}{2}, \frac{2.3+–9.4}{2}\right)=\left(–10, –3.55\right) ✓ \end{gathered}$$