Question

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (XY) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y)

midpoint (5. - 12), endpoint (4-7)
The other endpoint is
(Type an ordered pair)

Answer 1

(6, -17)

Explanation:

Given the coordinate of a midpoint, (5, -12), and one endpoint, (4, -7), the other endpoint can be determined as follows:

The midpoint formula is given as
`M((x_1 + x_2)/(2), (y_1 + y_2)/(2))`.

Since we are given ordered pairs of the midpoint and one endpoint, we would find the other ordered pair of the endpoint as shown below.

Let the other endpoint be
`(x_1, y_1)`

Midpoint = M(5, -12)

Let the given endpoint =
`(4, -7) = (x_2, y_2)`

Thus:

`M(5, -12) = ((x_1 + 4)/(2), (y_1 +(-7))/(2))`

Rewrite the equation to find the coordinates of the other endpoints

`5 = (x_1 + 4)/(2)` and
`-12 = (y_1 - 7)/(2)`

Solve for each:

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

`5*2 = (x_1 + 4)/(2)*2`

`10 = x_1 + 4`

`10 - 4 = x_1 + 4 - 4`

`6 = x_1`

`x_1 = 6`

`-12 = (y_1 - 7)/(2)`

`-12*2 = (y_1 - 7)/(2)*2`

`-24 = y_1 - 7`

`-24 + 7 = y_1 - 7 + 7`

`-17 = y_1`

`y_1 = -17`

Ordered pair of the other endpoint is (6, -17)