Question

Midpoint Formula Homework Given the midpoint and one endpoint of a line segment, find the other endpoint. Endpoint:(-8, -10), midpoint:(10, -7)

Answer 1

We are given the midpoint and one endpoint of a line segment.

Midpoint = (10, -7)

Endpoint = (-8, -10)

We are asked to find the other endpoint.

Recall that the midpoint formula is given by

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

Let us solve for the other endpoint (x₂, y₂)

$\begin{gathered} x_m=\frac{x_1+x_2}{2} \\ 10=\frac{-8+x_2}{2} \\ 10\cdot2=-8+x_2 \\ 20=-8+x_2 \\ 20+8=x_2 \\ x_2=28 \end{gathered}$

Similarly,

$\begin{gathered} y_m=\frac{y_1+y_2}{2} \\ -7=\frac{-10_{}+y_2}{2} \\ -7\cdot2=-10_{}+y_2 \\ -14=-10_{}+y_2 \\ -14+10=y_2 \\ y_2=-4 \end{gathered}$

Therefore, the other endpoint is

$(x_2,y_2)=(28,-4)$