Question

the midpoint m of $overline{gh}$ has coordinates (-8.5, -3.5). point h has coordinates (-6, -7). 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 $(-6,-7)$ and the mid - point $M$ be $(-8.5,-3.5)$.

Step2: Solve for the x - coordinate of G

We know that $\frac{x+( - 6)}{2}=-8.5$. Multiply both sides by 2: $x - 6=-17$. Then add 6 to both sides: $x=-17 + 6=-11$.

Step3: Solve for the y - coordinate of G

We know that $\frac{y+( - 7)}{2}=-3.5$. Multiply both sides by 2: $y - 7=-7$. Then add 7 to both sides: $y=-7 + 7 = 0$.

Answer:

$(-11,0)$