Question

the midpoint m of $overline{fg}$ has coordinates (-15.4, 2.8). point f has coordinates (-13.5, 8.9). find the coordinates of point g. write the coordinates as decimals or integers. g = ( , )

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $F=(x_1,y_1)=(-13.5,8.9)$ and $G=(x_2,y_2)$, and $M=(-15.4,2.8)$.

Step2: Solve for x - coordinate of G

We know that $\frac{x_1 + x_2}{2}=x_M$. Substitute $x_1=-13.5$ and $x_M=-15.4$ into the formula:
$\frac{-13.5 + x_2}{2}=-15.4$. Multiply both sides by 2: $-13.5 + x_2=-15.4\times2=-30.8$. Then $x_2=-30.8 + 13.5=-17.3$.

Step3: Solve for y - coordinate of G

We know that $\frac{y_1 + y_2}{2}=y_M$. Substitute $y_1 = 8.9$ and $y_M=2.8$ into the formula:
$\frac{8.9 + y_2}{2}=2.8$. Multiply both sides by 2: $8.9 + y_2=2.8\times2 = 5.6$. Then $y_2=5.6 - 8.9=-3.3$.

Answer:

$G=(-17.3,-3.3)$