Question

find the midpoint of the line segment with the given endpoints. (4,5√7) and (-10,√7)
the midpoint of the segment is . (type an ordered pair. type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1 = 4$, $x_2=-10$, $y_1 = 5\sqrt{7}$, $y_2=\sqrt{7}$.

Step2: Calculate the x - coordinate of the mid - point

$\frac{x_1 + x_2}{2}=\frac{4+( - 10)}{2}=\frac{4 - 10}{2}=\frac{-6}{2}=-3$.

Step3: Calculate the y - coordinate of the mid - point

$\frac{y_1 + y_2}{2}=\frac{5\sqrt{7}+\sqrt{7}}{2}=\frac{(5 + 1)\sqrt{7}}{2}=\frac{6\sqrt{7}}{2}=3\sqrt{7}$.

Answer:

$(-3,3\sqrt{7})$