Question

1. practice: organizing information and summarizing

fill in the blanks to complete the list.
midpoint of diagonal segment

• -coordinate = average of -coordinates of endpoints
• -coordinate = average of -coordinates of endpoints

1. practice: using visual cues

fill in the blanks to explain the midpoint formula.
midpoint formula
midpoint = ($\frac{x_1 + x_2}{2}$, $\frac{y_1 + y_2}{2}$)
($x_1,y_1$) = first
($x_2,y_2$) = second
$\frac{x_1 + x_2}{2}$ = of x - coordinates
$\frac{y_1 + y_2}{2}$ = of y - coordinates

1. practice: making mental images

find the midpoint of each segment. show your work.

1. segment endpoints: (0, 0) and (-8, 6)
2. segment endpoints: (-1, 7) and (3, -3)

midpoint =
midpoint =

1. practice: drawing inferences

show that the fractional distance formula for any point p between two points a and b on the number line

Explanation:

Step1: Fill in blanks for mid - point concept

The $x$-coordinate of the mid - point of a line segment is the average of the $x$-coordinates of the endpoints, and the $y$-coordinate of the mid - point of a line segment is the average of the $y$-coordinates of the endpoints.

Step2: Fill in blanks for mid - point formula

In the mid - point formula midpoint=$(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$, $(x_1,y_1)$ is the first endpoint, $(x_2,y_2)$ is the second endpoint, $\frac{x_1 + x_2}{2}$ is the average of $x$-coordinates and $\frac{y_1 + y_2}{2}$ is the average of $y$-coordinates.

Step3: Find mid - point for segment with endpoints $(0,0)$ and $(-8,6)$

Use the mid - point formula:
$x=\frac{0+( - 8)}{2}=\frac{-8}{2}=-4$
$y=\frac{0 + 6}{2}=3$
The mid - point is $(-4,3)$.

Step4: Find mid - point for segment with endpoints $(-1,7)$ and $(3,-3)$

Use the mid - point formula:
$x=\frac{-1 + 3}{2}=\frac{2}{2}=1$
$y=\frac{7+( - 3)}{2}=\frac{4}{2}=2$
The mid - point is $(1,2)$.

Answer:

1. $x$, $x$; $y$, $y$
2. endpoint, endpoint, average, average
3. 1. $(-4,3)$
4. $(1,2)$