Question

the midpoint of $overline{gh}$ is $m(-6.05, 8.8)$. one endpoint is $g(-18.7, 8.7)$. find the coordinates of the other endpoint $h$. write the coordinates as decimals or integers. $h = (square,square)$

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 $G(x_1,y_1)=(-18.7,8.7)$ and $H(x_2,y_2)$, and $M(-6.05,8.8)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=x_M$. Substitute $x_1=-18.7$ and $x_M = - 6.05$ into the formula:
$\frac{-18.7+x_2}{2}=-6.05$. Multiply both sides by 2: $-18.7 + x_2=-12.1$. Then $x_2=-12.1 + 18.7=6.6$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=y_M$. Substitute $y_1 = 8.7$ and $y_M=8.8$ into the formula:
$\frac{8.7+y_2}{2}=8.8$. Multiply both sides by 2: $8.7 + y_2 = 17.6$. Then $y_2=17.6 - 8.7 = 8.9$.

Answer:

$(6.6,8.9)$