Question

the midpoint of $overline{ab}$ is $m(-2,4)$. if the coordinates of $a$ are $(-1,5)$, 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 $x_1=-1,y_1 = 5$ and $M(-2,4)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-2$. Substitute $x_1=-1$ into it: $\frac{-1 + x_2}{2}=-2$. Multiply both sides by 2: $-1+x_2=-4$. Then add 1 to both sides: $x_2=-3$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=4$. Substitute $y_1 = 5$ into it: $\frac{5 + y_2}{2}=4$. Multiply both sides by 2: $5 + y_2=8$. Then subtract 5 from both sides: $y_2=3$.

Answer:

$(-3,3)$