Question

the midpoint of $overline{fg}$ is $(6, -4)$ and the coordinates of point f are $(-3, 6)$. what are the coordinates of point g? you must support your answer with evidence, but using the graph is optional.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let the coordinates of point $G$ be $(x,y)$, the coordinates of point $F$ be $(x_1,y_1)=(-3,6)$ and the mid - point be $(x_m,y_m)=(6,-4)$.

Step2: Solve for the x - coordinate of G

We know that $x_m=\frac{x_1 + x}{2}$. Substituting the known values: $6=\frac{-3 + x}{2}$. Multiply both sides by 2: $12=-3 + x$. Then add 3 to both sides: $x = 15$.

Step3: Solve for the y - coordinate of G

We know that $y_m=\frac{y_1 + y}{2}$. Substituting the known values: $-4=\frac{6 + y}{2}$. Multiply both sides by 2: $-8 = 6 + y$. Then subtract 6 from both sides: $y=-14$.

Answer:

$(15,-14)$