Question

Find the missing endpoint. Endpoint:(-9 -2) Midpoint:(-6,2)

Answer 1

The coordinates of the midpoint are the average of the coordinates of the endpoints.

So, for example, using the endpoints (x1, y1) and (x2, y2) and the midpoint (mx, my), we have that:

`\begin{gathered} mx_{}=(x_1+x_2)/(2) \\ my=(y_1+y_2)/(2) \end{gathered}`

Now, using the midpoint (-6, 2) and the endpoint (-9, -2), we have:

`\begin{gathered} mx=(x_1+x_2)/(2) \\ -6=(-9+x_2)/(2) \\ -9+x_2=-12 \\ x_2=-12+9=-3 \\ \\ my=(y_1+y_2)/(2) \\ 2=(-2+y_2)/(2) \\ -2+y_2=4_{} \\ y_2=4+2=6 \end{gathered}`

So the coordinates of the second endpoint are (-3, 6).