Question

The midpoint of a segment is (4,3) and one endpoint is (10,8) Find the coordinates of the other endpoint.

Answer 1

The answer is: (-2,-2). :)

Answer 2

`(-2,-2)`.

Explanation:

Let us assume that coordinates of other endpoint are
`(x_1,y_1)`

We have been given that the midpoint of a segment is (4,3) and one endpoint is (10,8). We are asked to find the coordinates of the other endpoint.

We will use midpoint formula to solve our given problem.

`x\text{-coordinate of midpoint}=(x_1+x_2)/(2)`

`y\text{-coordinate of midpoint}=(y_1+y_2)/(2)`

Upon using our given information, we will get:

`4=(x_1+10)/(2)`

`4\cdot 2=(x_1+10)/(2)\cdot 2`

`8=x_1+10`

`8-10=x_1+10-10`

`x_1=-2`

Similarly, we will find y-coordinate.

`3=(y_1+8)/(2)`

`3\cdot 2=(y_1+8)/(2)\cdot 2`

`6=y_1+8`

`6-8=y_1+8-8`

`y_1=-2`

Therefore, the coordinates of other endpoint would be
`(-2,-2)`.