Question

the midpoint of $overline{gh}$ is $m(0, 13)$. one endpoint is $h(12, 8)$. find the coordinates of the other endpoint $g$. 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 $G=(x,y)$ and $H=(12,8)$ and $M=(0,13)$.

Step2: Solve for x - coordinate

We know that $\frac{x + 12}{2}=0$. Cross - multiply: $x+12 = 0\times2=0$. Then $x=- 12$.

Step3: Solve for y - coordinate

We know that $\frac{y + 8}{2}=13$. Cross - multiply: $y + 8=13\times2 = 26$. Then $y=26 - 8=18$.

Answer:

$G=(-12,18)$