Question

the midpoint of fg is point h at (-5, 2). one endpoint is g(-9, -6). what is the y - coordinate of the other endpoint? the y - coordinate of the other endpoint is

Explanation:

Step1: Recall mid - point formula for y - coordinate

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $y_{mid}=\frac{y_1 + y_2}{2}$. Let the coordinates of $F$ be $(x,y)$ and the coordinates of $G$ be $(-9,-6)$ and the mid - point $H$ be $(-5,2)$. We are interested in the y - coordinate, so we use $y_{H}=\frac{y_{G}+y_{F}}{2}$.

Step2: Substitute known values into formula

We know that $y_{H} = 2$ and $y_{G}=-6$. Substituting into $y_{H}=\frac{y_{G}+y_{F}}{2}$, we get $2=\frac{-6 + y}{2}$.

Step3: Solve for y

Multiply both sides of the equation $2=\frac{-6 + y}{2}$ by 2: $2\times2=-6 + y$. So, $4=-6 + y$. Then add 6 to both sides: $y=4 + 6=10$.

Answer:

10