Answer: (1,16)
Step-by-step explanation:
The coordinates of a midpoint are given by the midpoint formula:
[tex](x_m, y_m) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex] where [tex](x_m,y_m)[/tex] is the ordered pair for the midpoint, [tex](x_1,y_1)[/tex] is the ordered pair for the first endpoint, and [tex](x_2,y_2)[/tex] is the ordered pair for the second endpoint.
In this problem, the midpoint is given as [tex](x_m,y_m) = (-3,7)[/tex]
The known endpoint of XY is X = [tex](x_1, y_1) = (-7, -2)[/tex]
Y remains unknown so Y = [tex](x_2, y_2)[/tex].
If the midpoint is given as (-3,7) we can compare the x value and the y value individually.
-3 = [tex]\frac{-7+x_2}{2}[/tex]
Solving for [tex]x_2[/tex], we get [tex]x_2[/tex] = 1.
7 = [tex]\frac{-2+y_2}{2}[/tex]
Solving for [tex]y_2[/tex], we get [tex]y_2[/tex] = 16.
Thus, the coordinates of Y are (1,16)
