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: Use 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 \(R(-10,8)\) be \((x_1,y_1)\) and \(V(x,y)\) be \((x_2,y_2)\), and \(E(6,-12)\).
For the \(x\) - coordinate: \(\frac{-10 + x}{2}=6\).

Step2: Solve for \(x\)

Multiply both sides by \(2\): \(-10 + x=12\). Then \(x = 12+10=22\).

Step3: Solve for \(y\)

For the \(y\) - coordinate: \(\frac{8 + y}{2}=-12\). Multiply both sides by \(2\): \(8 + y=-24\). Then \(y=-24 - 8=-32\).

Answer:

A. \((22,-32)\)