Question

select the correct answer. point e is the mid - point of 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 mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $E=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $R=(x_1,y_1)=(-10,8)$ and $V=(x_2,y_2)$. We know $E=(6,-12)$.

Step2: Solve for $x_2$

We have $\frac{x_1 + x_2}{2}=6$. Substitute $x_1=-10$ into the equation: $\frac{-10 + x_2}{2}=6$. Multiply both sides by 2: $-10+x_2 = 12$. Then $x_2=12 + 10=22$.

Step3: Solve for $y_2$

We have $\frac{y_1 + y_2}{2}=-12$. Substitute $y_1 = 8$ into the equation: $\frac{8 + y_2}{2}=-12$. Multiply both sides by 2: $8+y_2=-24$. Then $y_2=-24 - 8=-32$.

Answer:

A. $(22,-32)$