Section 1-7: Midpoint and Distance in the Coordinate Plane
Essential Question: How can we use the coordinate plane to find measurements of line
segments?
Do Now:
Midpoint Formula

Finding the __________ of the x-coordinates and the y-coordinates

If given two points, use the following formula to find the coordinates of the
midpoint:
Midpoint= (
,
)
Example 1: Finding the Midpoint
̅̅̅ has endpoints at -12 and 4 on a number line. What is the coordinate of its
a. 𝐽𝐾
midpoint?
b. What is the midpoint of ̅̅̅̅
𝑅𝑆 with endpoints R(5, -10) and S (3, 6)?
Example 2: Finding an Endpoint
The midpoint of ̅̅̅̅
𝐴𝐵 has coordinates (4, -9). Endpoint A has coordinates (-3, -5). What
are the coordinates of B?
Distance Formula
The distance between two points A(x1,y1) and B(x2,y2) is found by using the formula:
AB = √(
−
) +(
−
)
The distance formula is based on the ______________________ _________________.
Example 3- Applying the Distance Formula
̅̅̅̅ has endpoints S(-2,14) and R (3,-1).
𝑆𝑅
What is SR in exact form? To the nearest
tenth?
Use the diagram at the right to help
answer the question.
Example 4: Finding Distance and Midpoints
Use the given diagram to find the coordinates of the midpoint AND distance between
the two cities.
1. Colton and Riverton
Midpoint:
Distance:
2. Blakeville and Newton
Midpoint:
Distance:
Group Work:
2
̅̅̅̅ are A(-2, -3) and B(3, 2). Point C lies on AB and is of the way
1. The endpoints of 𝐴𝐵
5
from A to B. What are the coordinates of Point C? Explain how you found your answer.
2. Do you use the Midpoint Formula or the Distance Formula to find the following?
̅̅̅̅.
a. Given points K and P, find the distance from K to the midpoint of 𝐾𝑃
b. Given point K and the midpoint of ̅̅̅̅
𝐾𝑃, find KP.
3. You can use three coordinates (x, y, z) to locate points in three dimensions. Point P
has coordinates (6, -3, 9) as shown. Give the coordinates of points A, B, C, D, E, F, and
G.
HW: p. 54-55 # 17, 18, 31, 36-40 evens, 46-48, 57, 58