Question

1. practice: making mental images

find the midpoint of each segment. show your work.

1. segment endpoints: (0, 0) and (-8, 6)

midpoint =

1. segment endpoints: (-1, 7) and (3, - 13)

midpoint =

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: Solve for first segment

For points $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(-8,6)$, we have $x=\frac{0+( - 8)}{2}=\frac{-8}{2}=-4$ and $y=\frac{0 + 6}{2}=3$. So the mid - point is $(-4,3)$.

Step3: Solve for second segment

For points $(x_1,y_1)=(-1,7)$ and $(x_2,y_2)=(3,-13)$, we have $x=\frac{-1 + 3}{2}=\frac{2}{2}=1$ and $y=\frac{7+( - 13)}{2}=\frac{7 - 13}{2}=\frac{-6}{2}=-3$. So the mid - point is $(1,-3)$.

Answer:

1. $(-4,3)$
2. $(1,-3)$