Question

What is the other endpoint if one endpoint is (10,12) and the midpoint is (6,9).?

Answer 1

`(2,\, 6)`.

Explanation:

Let
`(x_(0),\, y_(0))` and
`(x_(1),\, y_(1))` denote the two endpoints.

The formula for the midpoint of these two points would be:

`\displaystyle \left((x_(0) + x_(1))/(2),\, (y_(0) + y_(1))/(2)\right)`.

(Similar to taking the average of each coordinate.)

In this question, it is given that
`x_(0) = 10` whereas
`y_(0) = 12`. Substitute these two values into the expression for the coordinate of the midpoint:

• 
  `x`-coordinate of the midpoint:
  `\displaystyle (10 + x_(1))/(2) = 6`.
• 
  `y`-coordinate of the midpoint:
  `\displaystyle (12 + y_(1))/(2) = 9`.

Solve these two equations for
`x_(1)` and
`y_(1)`:
`x_(1) = 2` whereas
`y_(1) = 6`.

Hence, the coordinate of the other point would be
`(2,\, 6)`.