Question

the midpoint of $overline{ab}$ is $m=(2, - 2)$. one endpoint is $a=(-3,2)$. find the coordinates of the other endpoint, $b$.

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 $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $A(-3,2)$ and $M(2,-2)$, let $B=(x,y)$.

Step2: Solve for the x - coordinate of B

We have $\frac{-3 + x}{2}=2$. Multiply both sides by 2: $-3 + x=4$. Then add 3 to both sides: $x = 4+3=7$.

Step3: Solve for the y - coordinate of B

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

Answer:

$(7,-6)$