Question

a line segment has an endpoint at (-7,11). If the midpoint of the line segment is (-6,4), what are the coordinates of the other endpoints?

Answer 1

Using the midpoint formula

`(x_m,y_m)=((x_1+x_2)/(2),(y_1+y_2)/(2))`

divide the formula for x and y and solve for x2 and y2.

`\begin{gathered} (-6,4)=((-7+x_2)/(2),(11+y_2)/(2)) \\ -6=(-7+x_2)/(2) \\ 4=(11+y_2)/(2) \end{gathered}`

solve for x2

`\begin{gathered} -6=(-7+x_2)/(2) \\ -12=-7+x_2 \\ -12+7=x_2 \\ x_2=-5 \end{gathered}`

solve for y2

`\begin{gathered} 4=(11+y_2)/(2) \\ 8=11+y_2 \\ 8-11=y_2 \\ y_2=-3 \end{gathered}`

The coordinates of the other endpoint is (-5,-3)