Question

the midpoint of $overline{ab}$ is $m(-1,0)$. if the coordinates of $a$ are $(6, - 4)$, 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 $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Solve for $x_2$

We know $M(-1,0)$, $A(6,-4)$. For the $x$ - coordinate of the mid - point: $\frac{6 + x_2}{2}=-1$. Multiply both sides by 2: $6 + x_2=-2$. Then subtract 6 from both sides: $x_2=-2 - 6=-8$.

Step3: Solve for $y_2$

For the $y$ - coordinate of the mid - point: $\frac{-4 + y_2}{2}=0$. Multiply both sides by 2: $-4 + y_2 = 0$. Then add 4 to both sides: $y_2 = 4$.

Answer:

$(-8,4)$