Question

find the midpoint of the line segment with the given endpoints. (6,7\sqrt{3}) and (-4,9\sqrt{3})
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 $x_1=6,y_1 = 7\sqrt{3},x_2=-4,y_2 = 9\sqrt{3}$.

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

$x=\frac{6+( - 4)}{2}=\frac{6 - 4}{2}=\frac{2}{2}=1$.

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

$y=\frac{7\sqrt{3}+9\sqrt{3}}{2}=\frac{(7 + 9)\sqrt{3}}{2}=\frac{16\sqrt{3}}{2}=8\sqrt{3}$.

Answer:

$(1,8\sqrt{3})$