Question

select the correct answer.
point e is the midpoint of \\(\overline{rv}\\). point e is located at (6,-12), and point r is located at (-10,8). where is point v located?
a. (22,-32)
b. (-26,28)
c. (-2,-2)
d. (-4,-4)
e. (-16,20)

Explanation:

Step1: Recall midpoint formula

The midpoint $E(x_E, y_E)$ of segment $\overline{RV}$ with endpoints $R(x_R, y_R)$ and $V(x_V, y_V)$ is given by:
$$x_E = \frac{x_R + x_V}{2}, \quad y_E = \frac{y_R + y_V}{2}$$

Step2: Solve for $x_V$

Substitute $x_E=6$, $x_R=-10$ into the x-coordinate formula:
$$6 = \frac{-10 + x_V}{2}$$
Multiply both sides by 2: $12 = -10 + x_V$
Solve for $x_V$: $x_V = 12 + 10 = 22$

Step3: Solve for $y_V$

Substitute $y_E=-12$, $y_R=8$ into the y-coordinate formula:
$$-12 = \frac{8 + y_V}{2}$$
Multiply both sides by 2: $-24 = 8 + y_V$
Solve for $y_V$: $y_V = -24 - 8 = -32$

Answer:

A. (22,-32)