Question

1. the midpoint of $overline{ab}$ is $m(-2, -5)$. if the coordinates of $a$ are $(1, -8)$, 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 $x_1 = 1,y_1=-8$ and $M(-2,-5)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-2$. Substitute $x_1 = 1$ into the equation: $\frac{1 + x_2}{2}=-2$. Multiply both sides by 2: $1+x_2=-4$. Then subtract 1 from both sides: $x_2=-4 - 1=-5$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=-5$. Substitute $y_1=-8$ into the equation: $\frac{-8 + y_2}{2}=-5$. Multiply both sides by 2: $-8 + y_2=-10$. Then add 8 to both sides: $y_2=-10 + 8=-2$.

Answer:

$(-5,-2)$