Question

Midpoint: 8, -2 Endpoint: 3,10 find other point

Answer 1

The midpoint coordinates are: (8,-2)

We can label this coordinates as follows

`\begin{gathered} x_m=8 \\ y_m=-2 \end{gathered}`

The coordinates for one of the endpoints are: (3,10)

We label this coordinates as follows:

`\begin{gathered} x_1=3 \\ y_1=10_{}_{} \end{gathered}`

We are looking for the other endpoints with the coordinates (x2,y2).

We use the formulas to find the midpoint:

`\begin{gathered} x_m=(x_1+x_2)/(2)_{} \\ y_m=(y_1+y_2)/(2) \end{gathered}`

But, since we need x2 and y2, we solve for then in the equations:

`\begin{gathered} 2x_m-x_1=x_2_{} \\ 2y_m-y_1=y_2 \end{gathered}`

And we substitute our values into the equations:

For x2:

`\begin{gathered} 2(8)-3=x_2 \\ 16-3=x_2 \\ 13=x_2 \end{gathered}`

For y2:

`\begin{gathered} 2(-2)-10=y_2 \\ -4-10=y_2 \\ -14=y_2 \end{gathered}`

Answer: (13,-14)