Question

the midpoint of $overline{ab}$ is $m(-6,6)$. if the coordinates of $a$ are $(-4,4)$, 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 $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1=-4,y_1 = 4$, and $M(-6,6)$.

Step2: Find the x - coordinate of B

Set up the equation for the x - coordinate of the mid - point: $\frac{-4+x_2}{2}=-6$. Multiply both sides by 2: $-4 + x_2=-12$. Then add 4 to both sides: $x_2=-12 + 4=-8$.

Step3: Find the y - coordinate of B

Set up the equation for the y - coordinate of the mid - point: $\frac{4+y_2}{2}=6$. Multiply both sides by 2: $4 + y_2 = 12$. Then subtract 4 from both sides: $y_2=12 - 4 = 8$.

Answer:

$(-8,8)$