Question

the midpoint m of gh has coordinates (67.5, 47). point h has coordinates (56, 14). 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 the coordinates of point $G$ be $(x,y)$ and point $H=(56,14)$ and mid - point $M=(67.5,47)$.

Step2: Solve for the x - coordinate of G

We know that $\frac{x + 56}{2}=67.5$. Multiply both sides by 2: $x + 56=135$. Then subtract 56 from both sides: $x=135 - 56=79$.

Step3: Solve for the y - coordinate of G

We know that $\frac{y + 14}{2}=47$. Multiply both sides by 2: $y + 14=94$. Then subtract 14 from both sides: $y=94 - 14=80$.

Answer:

$(79,80)$