Question

What are two ordered pairs that the midpoints (4, -10)? Please show that your points work.

Answer 1

In order to find any pair of points that have a midpoint of (4, -10), we can choose any two values p and q. Then, one of the endpoints will be (4+p, -10+q) and the other endpoint will be (4-p, -10-q).

For example, let's choose p = q = 2, so we have:

`\begin{gathered} midpoint\text{ \lparen4,-10\rparen}\\ \\ \\ \\ 1st\text{ endpoint:}\\ \\ (4+2,-10+2)=(6,-8)\\ \\ \\ \\ 2nd\text{ endpoint:}\\ \\ (4-2,-10-2)=(2,-12) \end{gathered}`

Therefore the ordered pairs (6, -8) and (2, -12) have a midpoint of (4, -10).