Question

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 the mid - point $M(3,3)$.

Step2: Find the x - coordinate of B

Set up the equation for the x - coordinate of the mid - point: $\frac{2 + x_2}{2}=3$. Cross - multiply: $2 + x_2=6$. Solve for $x_2$: $x_2=6 - 2=4$.

Step3: Find the y - coordinate of B

Set up the equation for the y - coordinate of the mid - point: $\frac{-2 + y_2}{2}=3$. Cross - multiply: $-2 + y_2 = 6$. Solve for $y_2$: $y_2=6 + 2=8$.

Answer:

$(4,8)$