Question

the midpoint of $overline{ab}$ is $m(-3,0)$. if the coordinates of $a$ are $(-5,3)$, 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 $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1=-5,y_1 = 3$ and $M(-3,0)$.

Step2: Find the x - coordinate of B

Set up the equation for the x - coordinate of the mid - point: $\frac{-5+x_2}{2}=-3$. Multiply both sides by 2: $-5 + x_2=-6$. Then add 5 to both sides: $x_2=-6 + 5=-1$.

Step3: Find the y - coordinate of B

Set up the equation for the y - coordinate of the mid - point: $\frac{3+y_2}{2}=0$. Multiply both sides by 2: $3 + y_2=0$. Then subtract 3 from both sides: $y_2=-3$.

Answer:

$(-1,-3)$