Question

XY has one endpoint at X(-7, -2) and its midpoint is M(-3,7). What are the coordinates of Y?

Answer 1

Answer: (1,16)

Step-by-step explanation:

The coordinates of a midpoint are given by the midpoint formula:

$(x_m, y_m) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ where  $(x_m,y_m)$ is the ordered pair for the midpoint,  $(x_1,y_1)$  is the ordered pair for the first endpoint, and $(x_2,y_2)$ is the ordered pair for the second endpoint.

In this problem, the midpoint is given as $(x_m,y_m) = (-3,7)$

The known endpoint of XY is X = $(x_1, y_1) = (-7, -2)$

Y remains unknown so Y =  $(x_2, y_2)$.

If the midpoint is given as (-3,7) we can compare the x value and the y value individually.

-3 = $\frac{-7+x_2}{2}$

Solving for $x_2$, we get $x_2$ = 1.

7 = $\frac{-2+y_2}{2}$

Solving for $y_2$, we get $y_2$ = 16.

Thus, the coordinates of Y are (1,16)