Question

practice: making mental images
find the midpoint of each segment. show your work.

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

midpoint =

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

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: Calculate mid - point for first segment

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

Step3: Calculate mid - point for second segment

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

Answer:

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