Question

find the midpoint of the line segment whose endpoints are given.
$(3\sqrt {5},-2\sqrt {6}),( - 3\sqrt {5},-\sqrt {6})$
the midpoint is
(type an ordered pair using exact answers. use radicals as needed.)

Explanation:

Step1: Find the x - coordinate of the midpoint

The formula for the x - coordinate of the midpoint \(M_x\) of two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(M_x=\frac{x_1 + x_2}{2}\).
Here, \(x_1 = 3\sqrt{5}\), \(x_2=-3\sqrt{5}\).
\(M_x=\frac{3\sqrt{5}+(-3\sqrt{5})}{2}=\frac{3\sqrt{5}-3\sqrt{5}}{2}=0\)

Step2: Find the y - coordinate of the midpoint

The formula for the y - coordinate of the midpoint \(M_y\) of two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(M_y=\frac{y_1 + y_2}{2}\).
Here, \(y_1=-2\sqrt{6}\), \(y_2 =-\sqrt{6}\).
\(M_y=\frac{-2\sqrt{6}+(-\sqrt{6})}{2}=\frac{-2\sqrt{6}-\sqrt{6}}{2}=\frac{-3\sqrt{6}}{2}\)

Answer:

\((0,-\frac{3\sqrt{6}}{2})\)