Question

the coordinates of the midpoint of $overline{gh}$ are $m(1,3)$ and the coordinates of one endpoint are $g(5, - 6)$. the coordinates of the other endpoint are ( ).

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 $G(x_1,y_1)=(5,-6)$ and $H(x_2,y_2)$ and $M(4,3)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=4$. Substitute $x_1 = 5$ into the equation: $\frac{5 + x_2}{2}=4$. Multiply both sides by 2: $5+x_2=8$. Then subtract 5 from both sides: $x_2=8 - 5=3$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=3$. Substitute $y_1=-6$ into the equation: $\frac{-6 + y_2}{2}=3$. Multiply both sides by 2: $-6 + y_2=6$. Then add 6 to both sides: $y_2=6 + 6 = 12$.

Answer:

$(3,12)$