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WEEK 32-GEOMETRIC-DISTANCE
VIMSCHOOL
Created on October 9, 2024
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Transcript
Geometric Distance
Objectives
Start
Story
Pythagorean Theorem
Calculation of Distance
Practice
Summary
Story
Pythagorean Theorem
Pythagorean theorem states the relationship between the lengths of the sides of a right triangle.
Theorem: The sum of the squared legs of a right triangle equals to the hypothenuse squared.
🗨️
a²+b²=c²
are the lenght of the sides.
a b
is the hypothenuse lenght .
Calculation of Distance
The distance, d, between two points in a coordinate plane can be calculated using the Pythagorean Theorem.
Definition: Distance betweenis:
(x₁,y₁) and (x₂,y₂)
🗨️
is the lenght of one leg.
|x₂-x₁|
Change of y
is the lenght of the other leg.
|y₂-y₁|
Change of x
Let's see some examples:
Example 1: Calculate the distance between points (3, 4) and (7, 1)
(x₁,y₁)=(3,4); (x₂,y₂)=(7,1)
d=5
Practice
Click here to draw >
Distance Between Two Points
Plot the points and trace a segment indicating the distance between the points.
Calculate the distance between points (-1, -2) and (5, 6)
(x₁,y₁)=(-1,-2); (x₂,y₂)=(5,6)
Solution
Click here to draw >
Distance Travelled
A car moved as shown in the figure. Find the total distance travelled by the car.
d=√50 km
(x₁,y₁)=(0,1); (x₂,y₂)=(5,5)
07:00
Try it by yourself:
Summary: Finding Distance Between Two Points
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See you next time
Welcome 6th graders!
A journey soon begin through Social Science experiences!
8TH-GEOMETRIC-DISTANCE-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0
MATERIAL
It is highly advised to have:
- Grid paper.
- A Protactor.
- Pencils of different colors.
- Eraser.
- A rule.
- A compass.
- A calculator.
- Geogebra installed on your phone/tablet/computer (or use online version).
"MA.8.GR.1 Develop an understanding of the Pythagorean Theorem and angle relationships involving triangles." MA.8.GR.1.2 Apply the Pythagorean Theorem to solve mathematical and real-world problems involving the distance between two points in a coordinate plane. MA.K12.MTR.7.1 Apply mathematics to real-world contexts. ELA.K12.EE.2.1 Read and comprehend grade-level complex texts proficiently.