Question

1. practice: making mental images

find the midpoint of each segment. show your work.

1. segment endpoints: (0, 0) and (0, 20)

midpoint = _

1. segment endpoints: (0, - 10) and (0, 20)

midpoint = _

Explanation:

Step1: Recall mid - point formula

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

Step2: Solve for the first segment

Given endpoints $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(0,20)$. Using the mid - point formula:
$x=\frac{0 + 0}{2}=0$, $y=\frac{0+20}{2}=10$. So the mid - point is $(0,10)$.

Step3: Solve for the second segment

Given endpoints $(x_1,y_1)=(0, - 10)$ and $(x_2,y_2)=(0,20)$. Using the mid - point formula:
$x=\frac{0 + 0}{2}=0$, $y=\frac{-10 + 20}{2}=5$. So the mid - point is $(0,5)$.

Answer:

1. $(0,10)$
2. $(0,5)$