Question

the midpoint of (overline{eg}) is (m(5, - 11)). one endpoint is (f(-6,-10)). find the coordinates of the other endpoint, (g). write the coordinates as decimals or integers. (g=(space,space))

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 $F(-6,-10)$ be $(x_1,y_1)$ and $G(x_2,y_2)$ be the unknown point, and $M(5,-11)$ be the mid - point.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting $x_1=-6$ and $x_M = 5$ into the formula: $\frac{-6+x_2}{2}=5$. Multiply both sides by 2: $-6 + x_2=10$. Then add 6 to both sides: $x_2=10 + 6=16$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting $y_1=-10$ and $y_M=-11$ into the formula: $\frac{-10+y_2}{2}=-11$. Multiply both sides by 2: $-10 + y_2=-22$. Then add 10 to both sides: $y_2=-22 + 10=-12$.

Answer:

$(16,-12)$