Question

point a is at (-7,5) and point m is at (0,4). 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 between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $A=(-7,5)$ be $(x_1,y_1)$ and $B=(x,y)$ be $(x_2,y_2)$ and $M=(0,4)$.

Step2: Solve for x - coordinate of B

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting $x_1=-7$ and $x_M = 0$, we get $\frac{-7+x}{2}=0$. Multiply both sides by 2: $-7 + x=0$, then $x = 7$.

Step3: Solve for y - coordinate of B

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting $y_1 = 5$ and $y_M=4$, we get $\frac{5 + y}{2}=4$. Multiply both sides by 2: $5 + y=8$, then $y=3$.

Answer:

$(7,3)$