Question

the midpoint of $overline{ab}$ is $m(-5,1)$. if the coordinates of $a$ are $(-3,3)$, 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 $A(-3,3)$ and $M(-5,1)$.

Step2: Find the x - coordinate of B

We know that $\frac{x_1 + x_2}{2}=x_M$. Substitute $x_1=-3$ and $x_M = - 5$ into the formula: $\frac{-3+x_2}{2}=-5$. Multiply both sides by 2: $-3 + x_2=-10$. Then add 3 to both sides: $x_2=-10 + 3=-7$.

Step3: Find the y - coordinate of B

We know that $\frac{y_1 + y_2}{2}=y_M$. Substitute $y_1 = 3$ and $y_M=1$ into the formula: $\frac{3+y_2}{2}=1$. Multiply both sides by 2: $3 + y_2=2$. Then subtract 3 from both sides: $y_2=2 - 3=-1$.

Answer:

$(-7,-1)$