Question

How do you find the coordinates of the other endpoint of a segment with the given Midpoint: (-4,6) and first Point: (-4,9)?

Answer 1

The other endpoint is at `(-4,3)`

Explanation:

The line segment passing through `(-4,9)` and `(-4,6)` is a vertical line with the midpoint `3` units below the first point.
The other endpoint must be `3` further units below the midpoint
i.e. at `(-4,(6-3))`

Answer 2

Other endpoint is `(-4,3)`

Explanation:

We could substitute the values we have into the the Midpoint formula. We will then be able to solve for the missing values.

`M((x_1+x_2)/2 ; (y_1 +y_2)/2) = (-4,6)`

However, we should notice that the x-values are the same..
This means this is a vertical line. The other end of the line segment is therefore on the same line. `x=-4`

The distance from the top endpoint to the midpoint is `9-6 = 3`

The other endpoint will therefore be 3 units below the midpoint.
`y = 3`

Other endpoint is `(-4,3)`