Question

What is the midpoint of a line segment with endpoints at (-4, 15) and (22,3)?

Answer 1

SOLUTION

First, let us list out the given:

$\begin{gathered} (-4,15)=(x_1,y_1) \\ x_1=-4 \\ y_1=15 \end{gathered}$$\begin{gathered} (22,3)=(x_2,y_2) \\ x_2=22 \\ y_2=3 \end{gathered}$

The formula for finding the midpoint of a line is:

$(x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Substituting the given into the formula above, we will have:

$\begin{gathered} (x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ (x_m,y_m)=(\frac{-4+22}{2},\frac{15+3}{2}) \\ (x_m,y_m)=(\frac{18}{2},\frac{18}{2}) \\ (x_m,y_m)=(9,9) \end{gathered}$

Therefore the midpoint of a line segment with endpoints at (-4, 15) and (22,3) is (9,9)