Question

the midpoint of $overline{gh}$ is $m(-9, -6)$. one endpoint is $g(-9, -5)$. 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 $G(x_1,y_1)=(-9,-5)$ and $H(x_2,y_2)$ and $M(-9,-6)$.

Step2: Find the x - coordinate of H

We know that $\frac{x_1 + x_2}{2}=-9$. Substitute $x_1=-9$ into the equation: $\frac{-9 + x_2}{2}=-9$. Multiply both sides by 2: $-9+x_2=-18$. Then add 9 to both sides: $x_2=-9$.

Step3: Find the y - coordinate of H

We know that $\frac{y_1 + y_2}{2}=-6$. Substitute $y_1 = - 5$ into the equation: $\frac{-5 + y_2}{2}=-6$. Multiply both sides by 2: $-5+y_2=-12$. Then add 5 to both sides: $y_2=-7$.

Answer:

$(-9,-7)$