Question

A line segment has an endpoint at (-5,8), and its midpoint is at (4,3). What is the ordered pair for the other endpoint of the line segment?

Answer 1

We have a line with two points, a conchoidal point, an endpoint and the midpoint.

Point A will be (-5,8) and the unknown endpoint which we will call B will be (x,y).

The midpoint of AB is (4,3), to find point B, We need to use our generalized midpoint formula:

`\begin{gathered} MP=((x_1+x_2)/(2),(y_1+y_2)/(2)) \\ \end{gathered}`

Now, we can replace the known values

`MP=((-5+x)/(2),(8+y)/(2))`

Solve each separately:

`\begin{gathered} (-5+x)/(2)=4 \\ x-5=4\cdot2 \\ x=8+5 \\ x=13 \end{gathered}`
`\begin{gathered} (8+y)/(2)=3 \\ y+8=3\cdot2 \\ y=6-8 \\ y=-2 \end{gathered}`

In conclusion, the ordered pair for the other endpoint of the line segment is:

`(13,-2)`