Question

point a is at (-7, -7) and point m is at (-6, -1). point m is the midpoint of point a and point b. what are the coordinates of point 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 $A(-7,-7)$ and $M(-6,-1)$. Let the coordinates of $B$ be $(x,y)$.

Step2: Solve for the x - coordinate of B

We know that $\frac{-7 + x}{2}=-6$. Multiply both sides by 2: $-7 + x=-12$. Then add 7 to both sides: $x=-12 + 7=-5$.

Step3: Solve for the y - coordinate of B

We know that $\frac{-7 + y}{2}=-1$. Multiply both sides by 2: $-7 + y=-2$. Then add 7 to both sides: $y=-2+7 = 5$.

Answer:

$(-5,5)$