Question

gh has a midpoint at m(8, 5). point g is at (9, 5). 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 $G(x_1,y_1)=(9,5)$ and $H(x_2,y_2)$, and $M(8,5)$.

Step2: Find the x - coordinate of H

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting $x_1 = 9$ and $x_M=8$ into $\frac{x_1 + x_2}{2}=x_M$, we get $\frac{9 + x_2}{2}=8$. Multiply both sides by 2: $9 + x_2=16$. Then subtract 9 from both sides: $x_2=16 - 9=7$.

Step3: Find the y - coordinate of H

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting $y_1 = 5$ and $y_M = 5$ into $\frac{y_1 + y_2}{2}=y_M$, we get $\frac{5 + y_2}{2}=5$. Multiply both sides by 2: $5 + y_2=10$. Then subtract 5 from both sides: $y_2=5$.

Answer:

$(7,5)$