Question

the midpoint of $overline{fg}$ is $m(8.8, 12.7)$. one endpoint is $g(5.1, 13.2)$. find the coordinates of the other endpoint $f$. write the coordinates as decimals or integers. $f = ( , )$

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 $F=(x,y)$ and $G=(5.1,13.2)$ and $M=(8.8,12.7)$.

Step2: Solve for x - coordinate of F

We have $\frac{x + 5.1}{2}=8.8$. Multiply both sides by 2: $x+5.1 = 17.6$. Then subtract 5.1 from both sides: $x=17.6 - 5.1=12.5$.

Step3: Solve for y - coordinate of F

We have $\frac{y + 13.2}{2}=12.7$. Multiply both sides by 2: $y + 13.2=25.4$. Then subtract 13.2 from both sides: $y=25.4 - 13.2 = 12.2$.

Answer:

$(12.5,12.2)$