Question

1. the endpoints of $overline{ab}$ are $a(-6,5)$ and $b(-1,-6)$. find the coordinates of the mid - point, $m$.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Identify the values of $x_1,y_1,x_2,y_2$

Here $x_1=-6,y_1 = 5,x_2=-1,y_2=-6$.

Step3: Calculate the x - coordinate of the mid - point

$x=\frac{-6+( - 1)}{2}=\frac{-6 - 1}{2}=\frac{-7}{2}=-\frac{7}{2}$.

Step4: Calculate the y - coordinate of the mid - point

$y=\frac{5+( - 6)}{2}=\frac{5 - 6}{2}=-\frac{1}{2}$.

Answer:

$M(-\frac{7}{2},-\frac{1}{2})$