Question

find the midpoint of the line segment whose endpoints are given.
(-1, -6), (5,4)

the midpoint is \boxed{}.
(simplify your answer.)

Explanation:

Step1: Calculate 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, \(x_1=-1\) and \(x_2 = 5\), so \(M_x=\frac{-1+5}{2}=\frac{4}{2}=2\).

Step2: Calculate 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, \(y_1=-6\) and \(y_2 = 4\), so \(M_y=\frac{-6 + 4}{2}=\frac{-2}{2}=-1\).

Answer:

\((2,-1)\)