Question

gh has a midpoint at m(8.5, 10.5). point g is at (15, 14). find the coordinates of point h. write the coordinates as decimals or integers. h = ( , )

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 $G(x_1,y_1)=(15,14)$ and $H(x_2,y_2)$. The mid - point $M(8.5,10.5)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=8.5$ and $x_1 = 15$. Substitute $x_1$ into the formula: $\frac{15 + x_2}{2}=8.5$. Multiply both sides by 2: $15 + x_2=17$. Then subtract 15 from both sides: $x_2=17 - 15=2$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=10.5$ and $y_1 = 14$. Substitute $y_1$ into the formula: $\frac{14 + y_2}{2}=10.5$. Multiply both sides by 2: $14 + y_2=21$. Then subtract 14 from both sides: $y_2=21 - 14 = 7$.

Answer:

$(2,7)$