For the points P and Q, find the coordinates of the midpoint of the segment PQ.
-$\mathrm { P } ( 5 \sqrt { 3 } , - \sqrt { 10 } ) , \mathrm { Q } ( - \sqrt { 3 } , 0 )$
A) $\left( 2 \sqrt { 3 } , - \frac { \sqrt { 10 } } { 2 } \right)$
B) $( - 3,10 )$
C) $\left( 2 \sqrt { 6 } , - \frac { \sqrt { 30 } } { 2 } \right)$
D) $\left( 3 \sqrt { 3 } , \frac { \sqrt { 10 } } { 2 } \right)$

Question

Quizplus · Accepted Answer

The midpoint formula is $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$. Applying this to the given points $P(5\sqrt{3}, -\sqrt{10})$ and $Q(-\sqrt{3}, 0)$, we get the midpoint coordinates as $\left( \frac{5\sqrt{3} - \sqrt{3}}{2}, \frac{-\sqrt{10} + 0}{2} \right) = \left( 2\sqrt{3}, -\frac{\sqrt{10}}{2} \right)$.

For the Points P and Q, Find the Coordinates of the Midpoint