Find the midpoint of the line segment whose endpoints are given.
-( $( 5 \sqrt { 2 } , 5 \sqrt { 5 } ) , ( 8 \sqrt { 2 } , 10 \sqrt { 5 } )$
A) $\left( \frac { - 3 \sqrt { 2 } } { 2 } , \frac { - 5 \sqrt { 5 } } { 2 } \right)$
B) $\left( \frac { 3 \sqrt { 2 } } { 2 } , \frac { 5 \sqrt { 5 } } { 2 } \right)$
C)( $( 13 \sqrt { 2 } , 15 \sqrt { 5 } )$
D) $\left( \frac { 13 \sqrt { 2 } } { 2 } , \frac { 15 \sqrt { 5 } } { 2 } \right)$

Question

Quizplus · Accepted Answer

The midpoint of a line 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 $(5\sqrt{2}, 5\sqrt{5})$ and $(8\sqrt{2}, 10\sqrt{5})$ results in $\left( \frac{5\sqrt{2} + 8\sqrt{2}}{2}, \frac{5\sqrt{5} + 10\sqrt{5}}{2} \right) = \left( \frac{13\sqrt{2}}{2}, \frac{15\sqrt{5}}{2} \right)$.

Find the Midpoint of the Line Segment Whose Endpoints Are (52,55),(82,105)( 5 \sqrt { 2 } , 5 \sqrt { 5 } ) , ( 8 \sqrt { 2 } , 10 \sqrt { 5 } )(52​,55​),(82​,105​)

Find the Midpoint of the Line Segment Whose Endpoints Are $( 5 \sqrt { 2 } , 5 \sqrt { 5 } ) , ( 8 \sqrt { 2 } , 10 \sqrt { 5 } )$