Question

1. find the coordinates of the midpoint of the segment with each pair of endpoints.

a. (-17, - 8) and (-1, 11)
b. (14, -7) and (-3, 18)

Explanation:

Step1: Recall mid - point formula

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

Step2: Calculate mid - point for part a

For endpoints $(-17,-8)$ and $(-1,11)$, $x_1=-17$, $y_1 = - 8$, $x_2=-1$, $y_2 = 11$.
$x=\frac{-17+( - 1)}{2}=\frac{-17 - 1}{2}=\frac{-18}{2}=-9$
$y=\frac{-8 + 11}{2}=\frac{3}{2}=1.5$
The mid - point is $(-9,1.5)$.

Step3: Calculate mid - point for part b

For endpoints $(14,-7)$ and $(-3,18)$, $x_1 = 14$, $y_1=-7$, $x_2=-3$, $y_2 = 18$.
$x=\frac{14+( - 3)}{2}=\frac{14 - 3}{2}=\frac{11}{2}=5.5$
$y=\frac{-7 + 18}{2}=\frac{11}{2}=5.5$
The mid - point is $(5.5,5.5)$.

Answer:

a. $(-9,1.5)$
b. $(5.5,5.5)$