Question

the midpoint of $overline{ab}$ is $m(3,3)$. if the coordinates of $a$ are $(2, - 2)$, 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 $x_1 = 2,y_1=-2$, and $M(3,3)$ so $\frac{x_1 + x_2}{2}=3$ and $\frac{y_1 + y_2}{2}=3$.

Step2: Solve for $x_2$

We have $\frac{2 + x_2}{2}=3$. Multiply both sides by 2: $2 + x_2=6$. Then subtract 2 from both sides: $x_2=6 - 2=4$.

Step3: Solve for $y_2$

We have $\frac{-2 + y_2}{2}=3$. Multiply both sides by 2: $-2 + y_2=6$. Then add 2 to both sides: $y_2=6 + 2 = 8$.

Answer:

$(4,8)$