Question

gh has a midpoint at m(-9.5, -4.5). point h is at (-15, -11). 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 $H(-15,-11)$ and mid - point $M(-9.5,-4.5)$.

Step2: Solve for x - coordinate of G

We know that $\frac{x+( - 15)}{2}=-9.5$. Multiply both sides by 2: $x - 15=-19$. Then add 15 to both sides: $x=-19 + 15=-4$.

Step3: Solve for y - coordinate of G

We know that $\frac{y+( - 11)}{2}=-4.5$. Multiply both sides by 2: $y-11=-9$. Then add 11 to both sides: $y=-9 + 11 = 2$.

Answer:

$G=(-4,2)$