Question

question
the midpoint of $overline{ab}$ is $m(-3,1)$. 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 $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $A(1,6)$ and $M(-3,1)$, and $B(x,y)$. Then $\frac{1 + x}{2}=-3$ and $\frac{6 + y}{2}=1$.

Step2: Solve for $x$

Solve the equation $\frac{1 + x}{2}=-3$. Multiply both sides by 2: $1 + x=-6$. Subtract 1 from both sides: $x=-6 - 1=-7$.

Step3: Solve for $y$

Solve the equation $\frac{6 + y}{2}=1$. Multiply both sides by 2: $6 + y = 2$. Subtract 6 from both sides: $y=2 - 6=-4$.

Answer:

$(-7,-4)$