Question

A segment has a midpoint at (2,-7) and an endpoint at (8,-5). What are the coordinates of the other endpoint?

Answer 1

To find the coordinates of the other endpoint, use the midpoint formula to average the x-coordinates and the y-coordinates of the given point and the midpoint.

Step-by-step explanation:

To find the coordinates of the other endpoint, we can use the midpoint formula. The midpoint formula states that the midpoint of a line segment is the average of the x-coordinates and the average of the y-coordinates of the endpoints. So, we can calculate the x-coordinate of the other endpoint by averaging the x-coordinates of the given point and the midpoint: (8 + 2) / 2 = 5. Similarly, we can calculate the y-coordinate of the other endpoint by averaging the y-coordinates: (-5 + (-7)) / 2 = -6.

Therefore, the coordinates of the other endpoint are (5, -6).

Answer 2

(-4,-9)

Step-by-step explanation:

Given a segment AB with endpoints with coordinates

A:
`(x_A,y_A)`

B:
`(x_B,y_B)`

The coordinates of the midpoint M of the segment AB are given by:

`x_M = x_A + (x_B-x_A)/(2)\\y_M = y_A + (y_B-y_A)/(2)` (1)

In this problem, we know that:

- The midpoint of the segment AB has coordinates

`x_M=2\\y_M=-7`

- One of the endpoint of the segment has coordinates

`x_B=8\\y_B=-5`

So we can find the coordinates of the other endpoint A by re-arranging eq.(1) above:

`x_A=2x_M-x_B\\y_A=2y_M-y_B`

And substituting, we find:

`x_A=2(2)-8=-4\\y_A=2(-7)-(-5)=-9`

So, the coordinates of the other endpoint are (-4,-9).