Find the M is the midpoint of the line segment PQ, what is the coordinates of point Q? P (4, 5), M (-2, -3)

Find the M is the midpoint of the line segment PQ, what is the coordinates of point Q? P (4, 5), M (-2, -3)

Answers:

\(a. (2,2) \\ b. (6,8) \\ c. (-8,-11) \\ d. (-8,-15) \\ e. (-4, -7.5) \\\)

\(\begin{array}{|rcll|} \hline \frac{\vec{P} + \vec{Q}} {2} &=& \vec{M} \quad & | \quad \cdot 2\\\\ \vec{P} + \vec{Q} &=& 2\cdot \vec{M} \quad & | \quad - \vec{P} \\\\ \vec{Q} &=& 2\cdot \vec{M} - \vec{P} \quad & | \quad \vec{M} = \binom{-2}{-3} \quad \vec{P} = \binom{4}{5}\\\\ \vec{Q} &=& 2\cdot \binom{-2}{-3} - \binom{4}{5} \\\\ \vec{Q} &=& \binom{-2\cdot 2}{-3\cdot 2} - \binom{4}{5} \\\\ \vec{Q} &=& \binom{-4}{-6} - \binom{4}{5} \\\\ \vec{Q} &=& \binom{-4-4}{-6-5} \\\\ \mathbf{ \vec{Q} } &\mathbf{=} & \mathbf{ \binom{-8}{-11} } \\\\ \hline \end{array}\)

Point Q is  (-8, -11)

(c.)

Find the M is the midpoint of the line segment PQ, what is the coordinates of point Q? P (4, 5), M (-2, -3)