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

Jul 28, 2016

The other endpoint is at $\left(- 4 , 3\right)$

#### Explanation:

The line segment passing through $\left(- 4 , 9\right)$ and $\left(- 4 , 6\right)$ 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 $\left(- 4 , \left(6 - 3\right)\right)$

Jul 28, 2016

Other endpoint is $\left(- 4 , 3\right)$

#### 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 $\left(- 4 , 3\right)$