Question

the midpoint of $overline{ab}$ is $m(1, -7)$. if the coordinates of $a$ are $(-2, -6)$, what are the coordinates of $b$?

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $A(-2,-6)$ and $M(1,-7)$, and $B(x,y)$.

Step2: Solve for the x - coordinate of B

We know that $\frac{-2 + x}{2}=1$. Multiply both sides by 2: $-2 + x=2$. Then add 2 to both sides: $x = 4$.

Step3: Solve for the y - coordinate of B

We know that $\frac{-6 + y}{2}=-7$. Multiply both sides by 2: $-6 + y=-14$. Then add 6 to both sides: $y=-8$.

Answer:

$(4,-8)$