Question

gh has a midpoint at m(-2.5, 25). point h is at (8, 35). 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 $H(8,35)$ and mid - point $M(-2.5,25)$.

Step2: Solve for the x - coordinate of G

We know that $\frac{x + 8}{2}=-2.5$. Multiply both sides by 2: $x + 8=-2.5\times2=-5$. Then subtract 8 from both sides: $x=-5 - 8=-13$.

Step3: Solve for the y - coordinate of G

We know that $\frac{y + 35}{2}=25$. Multiply both sides by 2: $y + 35=25\times2 = 50$. Then subtract 35 from both sides: $y=50 - 35 = 15$.

Answer:

$(-13,15)$