Question

find the midpoint of the line segment with the given endpoints. (2,5\sqrt{7}) and (-4,7\sqrt{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 $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Identify $x_1,x_2,y_1,y_2$

Here $x_1 = 2$, $x_2=-4$, $y_1 = 5\sqrt{7}$, $y_2 = 7\sqrt{7}$.

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

$x=\frac{2+( - 4)}{2}=\frac{2 - 4}{2}=\frac{-2}{2}=-1$.

Step4: Calculate the y - coordinate of the mid - point

$y=\frac{5\sqrt{7}+7\sqrt{7}}{2}=\frac{(5 + 7)\sqrt{7}}{2}=\frac{12\sqrt{7}}{2}=6\sqrt{7}$.

Answer:

$(-1,6\sqrt{7})$