Question

Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint 1: (-6, 1) Midpoint: (-2,5) Endpoint 2= ​

Answer 1

Endpoint 2 = (2,9)

Explanation:

Pre-Solving

We are given that a line segment has one endpoint as (-6, 1).

We also know that the midpoint of the line segment is (-2, 5).
We want to find the value of endpoint 2.

Recall that the midpoint formula is
`((x_1+x_2)/(2) , (y_1+y_2)/(2) )`, where
`(x_1, y_1)` and
`(x_2, y_2)` are the endpoints.

As we know the value of the first endpoint and the midpoint, we can use their values to help find the second endpoint.

Solving

x-value

The x value of the midpoint, -2 is equal to
`(x_1+x_2)/(2)`

We can substitute -6 as
`x_1` and leave
`x_2` as the value of x in endpoint 2.

So:

`-2 = (-6 + x_2)/(2)`

Multiply both sides by 2.

`-4 = -6 + x_2`

Add -6 to both sides.

`2 = x_2`

y-value

The y value of the midpoint, 5 is equal to
`(y_1+y_2)/(2)`

We can substitute 1 as
`y_1` and leave
`y_2` as the value of y in endpoint 2.

So:

`5 = (1+y_2)/(2)`

Multiply both sides by 2.

`10 = 1 + y_2`

Subtract 1 from both sides.

`9 = y_2`

Answer

So,
`x_2=2` and
`y_2=9`. As a point, it is (2, 9).