Question

question
the midpoint of $overline{ab}$ is $m(-2,4)$. if the coordinates of $a$ are $(-1,6)$, 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 $A(-1,6)$ and $M(-2,4)$, let the coordinates of $B$ be $(x,y)$.

Step2: Solve for $x$ - coordinate of $B$

We have $\frac{-1 + x}{2}=-2$. Multiply both sides by 2: $-1 + x=-4$. Then add 1 to both sides: $x=-4 + 1=-3$.

Step3: Solve for $y$ - coordinate of $B$

We have $\frac{6 + y}{2}=4$. Multiply both sides by 2: $6 + y = 8$. Then subtract 6 from both sides: $y=8 - 6 = 2$.

Answer:

$(-3,2)$