Question

the midpoint of $overline{ab}$ is $m=(3, - 1)$. one endpoint is $a=(8, - 5)$. find the coordinates of the other endpoint, $b$.

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 $A=(8,-5)$ and $M=(3,-1)$. Let $B=(x,y)$.

Step2: Solve for x - coordinate of B

We know that $\frac{8 + x}{2}=3$. Cross - multiply: $8 + x=6$. Then subtract 8 from both sides: $x=6 - 8=-2$.

Step3: Solve for y - coordinate of B

We know that $\frac{-5 + y}{2}=-1$. Cross - multiply: $-5 + y=-2$. Then add 5 to both sides: $y=-2 + 5 = 3$.

Answer:

$(-2,3)$