Question

gh has a midpoint at m(3, 10). point h is at (4, 17). 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 $H(4,17)$ and mid - point $M(3,10)$.

Step2: Solve for $x$ - coordinate of $G$

We have $\frac{x + 4}{2}=3$. Multiply both sides by 2: $x + 4=6$. Then subtract 4 from both sides: $x=6 - 4=2$.

Step3: Solve for $y$ - coordinate of $G$

We have $\frac{y + 17}{2}=10$. Multiply both sides by 2: $y + 17=20$. Then subtract 17 from both sides: $y=20 - 17 = 3$.

Answer:

$(2,3)$