Question

the midpoint m of $overline{gh}$ has coordinates (5.5, 2). point h has coordinates (-4, 20). 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 $(-4,20)$ and the mid - point $M$ be $(5.5,2)$.

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: $x=11 + 4=15$.

Step3: Solve for the y - coordinate of G

We know that $\frac{y + 20}{2}=2$. Multiply both sides by 2: $y+20 = 4$. Then subtract 20 from both sides: $y=4 - 20=-16$.

Answer:

$(15,-16)$