For the points P and Q, find the coordinates of the midpoint of the segment PQ.
-$$P ( 5 \sqrt { 5 } , \sqrt { 11 } ) , Q ( - \sqrt { 5 } , 4 \sqrt { 11 } )$$
A) $( 2 \sqrt { 5 } , 5 \sqrt { 11 } )$
B) $\left( 2 \sqrt { 10 } , - \frac { \sqrt { 33 } } { 2 } \right)$
C) $\left( 2 \sqrt { 5 } , \frac { 5 \sqrt { 11 } } { 2 } \right)$
D) $\left( 3 \sqrt { 5 } , \frac { \sqrt { 11 } } { 2 } \right)$

Question

Quizplus · Accepted Answer

The midpoint of a segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$. Applying this formula to the given points $P(5\sqrt{5}, \sqrt{11})$ and $Q(-\sqrt{5}, 4\sqrt{11})$, we get the midpoint as $\left(\frac{5\sqrt{5} - \sqrt{5}}{2}, \frac{\sqrt{11} + 4\sqrt{11}}{2}\right) = \left(2\sqrt{5}, \frac{5\sqrt{11}}{2}\right)$.

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