Question

the midpoint of $overline{ab}$ is $m(-3, -2)$. if the coordinates of $a$ are $(1, -7)$, 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 $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $A(1,-7)$ and $M(-3,-2)$. Let the coordinates of $B$ be $(x,y)$.

Step2: Solve for x - coordinate

We have $\frac{1 + x}{2}=-3$. Cross - multiply: $1 + x=-6$. Then $x=-6 - 1=-7$.

Step3: Solve for y - coordinate

We have $\frac{-7 + y}{2}=-2$. Cross - multiply: $-7 + y=-4$. Then $y=-4 + 7 = 3$.

Answer:

$(-7,3)$