Question

gh has a mid - point at m(-5.5, 10.5). point h is at (-4, 8). 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 the coordinates of point $H$ be $(-4,8)$ and the mid - point $M$ be $(-5.5,10.5)$.

Step2: Solve for the x - coordinate of G

We know that $\frac{x+( - 4)}{2}=-5.5$. Multiply both sides by 2: $x - 4=-11$. Then add 4 to both sides: $x=-11 + 4=-7$.

Step3: Solve for the y - coordinate of G

We know that $\frac{y + 8}{2}=10.5$. Multiply both sides by 2: $y + 8 = 21$. Then subtract 8 from both sides: $y=21-8 = 13$.

Answer:

$G=(-7,13)$