Question

Find the other endpoint of the line segment with the given endpoint and midpoint.Endpoint: ( 6, 1), midpoint: ( -10, -3)

Answer 1

We know that

• Endpoint: (6, 1)

,

• Midpoint: (-10, -3)​

We use the midpoint formula to find the other end point.

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

Where,

`\begin{gathered} M=(-10,-3) \\ x_1=6 \\ y_1=1 \end{gathered}`

So, we have to find the coordinates for the second point. Let's replace all given information

`(-10,-3)=((6+x_2)/(2),(1+y_2)/(2))`

We solve x-coordinates and y-coordinates separately.

`\begin{gathered} (x_2+6)/(2)=-10 \\ x_2+6=-20 \\ x_2=-20-6=-26 \end{gathered}`
`\begin{gathered} (y_2+1)/(2)=-3 \\ y_2+1=-6 \\ y_2=-6-1 \\ y_2=-7 \end{gathered}`

Therefore, the other endpoint is (-26, -7).