Question

the midpoint of $overline{ab}$ is $m = (-4, -2)$. one endpoint is $a = (-7, 2)$. 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 $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $A(-7,2)$ and $M(-4,-2)$. Let the coordinates of $B$ be $(x,y)$.

Step2: Solve for x - coordinate

We know that $\frac{-7 + x}{2}=-4$. Multiply both sides by 2: $-7 + x=-8$. Then add 7 to both sides: $x=-8 + 7=-1$.

Step3: Solve for y - coordinate

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

Answer:

$(-1,-6)$