Question

the midpoint of $overline{ab}$ is $m(6, - 3)$. if the coordinates of $a$ are $(7, - 4)$, 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 $x_1 = 7,y_1=-4$ and $M(6,-3)$.

Step2: Find the x - coordinate of B

Set up the equation for the x - coordinate of the mid - point: $\frac{7 + x_2}{2}=6$. Multiply both sides by 2: $7 + x_2=12$. Then subtract 7 from both sides: $x_2=12 - 7=5$.

Step3: Find the y - coordinate of B

Set up the equation for the y - coordinate of the mid - point: $\frac{-4 + y_2}{2}=-3$. Multiply both sides by 2: $-4 + y_2=-6$. Then add 4 to both sides: $y_2=-6 + 4=-2$.

Answer:

$(5,-2)$