Question

The coordinates of midpoint M and endpoint Q of a segment are M(–7, 8) and Q(–19, 30). Find the coordinates of the other endpoint. (–31, 52) (–13, 19) (5, –14) (15, –4)

Answer 1

Answer:

Step-by-step explanation:

Use the midpoint formula to solve:

$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

We know the midpoint and one set of coordinates, so filling those in:

$(-7,8)=(\frac{x+(-19)}{2},\frac{y+30}{2})$

Since the -7 is the x coordinate of the midpoint, we set the x part of the equation equal to -7 and solve for x, and then do the same for y. The 2 equations are:

$-7=\frac{x-19}{2}$  and  $8=\frac{y+30}{2}$  We solve each one of these to get the x and y coordinates of the other endpoint. In both cases, multiply both sides of the equations by 2 and then solve by either adding or subtracting.

-14 = x - 19 so

5 = x

16 = y + 30 so

-14 = y

The coordinates of the other endpoint are (5, -14)