1.8 The Coordinate Plane Day #1: The Distance Formula
Big Idea: Measurement
Reasoning & Proof
Essential Question:
1. How is the distance between any two points on the coordinate plane calculated?
Learning Target #1: In today’s lesson, you will calculate the distance between any two points on the
coordinate plane by applying the distance formula.
Finding Distance on the Coordinate Plane:
You can think of a __________ as a dot,
and a _________ as a series of points.
In coordinate geometry you describe a point by an
____________ __________ represented by (x , y),
called the ___________________ of the _________.
Applying the Distance Formula:
Example 1: How far is the subway ride from Oak to Symphony?
Round to the nearest tenth. Each unit represents 1 mile.
LT#1: Look Fors:
Did you substitute the XCOORDINATES into one
set of parentheses and
the Y-COORDINATES in
the other set of
parentheses?
Do you understand LT#1?
Applying the Distance Formula:
Example 2: Find the distance between the points to the nearest tenth.
a. 𝐽(6, −2), 𝐾(−2,4)
b. 𝐿(12, −12), 𝑀(5,12)
Did you take the square
root?
1.8 The Coordinate Plane Day #2: Finding the Midpoint:
Big Idea: Measurement
Reasoning & Proof
Essential Questions:
1. How is the midpoint of a segment calculated?
2. How is the endpoint of a segment calculated if you know the other endpoint and its midpoint?
Learning Target #1: In today’s lesson, you will use two endpoints of a line segment to calculate its
midpoint.
To find the coordinate of the midpoint of a segment, find the ___________ or _________ of both the
x and y coordinates of the endpoints. Use the formula below.
Example 1: ̅̅̅̅
AB has endpoints (8,9)and (−6, −3). Find the coordinates of its midpoint M.
LT#1 Look Fors:
Do you understand LT#1?
Example 2: Find the coordinates of the midpoint of ̅̅̅̅
HX if 𝐻(−1, 5), 𝑋(9, −3).
Did you find the SUM
of the two x
coordinates? Did
you divide by 2?
Did you find the SUM
of the two ycoordinates? Did
you divide by 2?
Learning Target #2: We will also look at the problem in a different way. You will find the ENDPOINT of
a segment knowing the other endpoint and the midpoint.
Example 3: The midpoint of ̅̅̅̅
DG is M(−1,5). One endpoint is D(1,4).
Find the coordinates of the other endpoint G.
̅̅̅ has coordinates (5, -8).
Example 4: The coordinates of T are (1, 12). The midpoint of ̅𝑆𝑇
Find the coordinates of point S.
Do you understand LT#2?
Example 5: Find the coordinates of the midpoint ̅̅̅̅̅
𝑋𝑌 of with endpoints X(2, –5) and Y(6, 13).
Example 6: The midpoint of ̅̅̅̅
𝑋𝑌 has coordinates (4, –6). X has coordinates (2, –3).
Find the coordinates of Y
Extra Practice: Do you understand?
̅̅̅̅ has endpoints A(1, –3) and B(–4, 4). Find AB to the nearest tenth.
Example 7: 𝐴𝐵
Closure: Recall the distance and midpoint formulas.
These formulas MUST be memorized by the Chapter 1 Test.
Distance Formula = √(
)2 + (
)2
Midpoint Formula= (
,
)