Question

the midpoint of $overline{ab}$ is $m(3, - 5)$. 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 $M(3,-5)$.

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 subtract 5 from 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: $\frac{-3 + y_2}{2}=-5$. Multiply both sides by 2: $-3 + y_2=-10$. Then add 3 to both sides: $y_2=-10 + 3=-7$.

Answer:

$(1,-7)$