Question

Y is the midpoint of XZ. X has coordinates (2, 8), and Y has coordinates (–3, 10). Find the coordinates of Z.

Answer 1

The coordinates of Z is (-8,12)

Explanation:
`(2+x^(2) )/(2)= -3 \\(8+y^(2) )/(2) = 10`

You multiply -3 by 2 to get -6 then multiply 10 by 2 to get 20

then you create the equations
`2+x^(2) =-6\\8+y^(2) =20` you subtract 2 by -6 and you get -8 (x coordinate) and you subtract 8 by 20 to get 12 (y coordinate)

To check your answer you use the Midpoint formula
`((x^(1)+ x^(2) )/(2) )((y^(1)+y^(2))/(2)) =M`

`(2+-8)/(2) =(-6)/(2) = -3\\(8+12)/(2) =(20)/(2) =10` and you get your midpoint.