Uses of Pythagoras Theorem

Key Concepts

■ Apply the Pythagorean Theorem to find the distance between two points

■ Find the Perimeter of a figure on a coordinate plane

■ Use the Pythagorean Theorem to solve problems on the coordinate plane

Introduction:

In this chapter, we will learn the application of Pythagoras Theorem to find the distance between two points on a coordinate plane, application of Pythagoras Theorem to find the perimeter of a figure on a coordinate plane and application of Pythagoras Theorem to solve problems on a coordinate plane. 

7.4 Find Distance in the Coordinate Plane 

7.4.1 Apply the Pythagorean Theorem to find the distance between two points 

Example1: 

Kelly leaves school to go home. She walks 6 blocks North and then 8 blocks west. How can you use Pythagorean Theorem to find the distance between Kelly’s school and her home? 

Solution: 

Step 1: Plot and label the locations of the school and home on a coordinate plane. Use both the buildings as vertices and draw a right triangle. 

Step 2: Use Pythagorean Theorem to find the distance between the two buildings. 

The distance from school to home is 10 blocks. 

Example 2: 

Use the Pythagorean Theorem to calculate the length of the line shown on the provided coordinate plane. Round the answer to the nearest tenth. 

Solution: 

Step 1: Plot and label the two vertices of the line. Use both the vertices and draw a right triangle. 

In this equation: a and b are legs. c is hypotenuse 

Step 2: Use the Pythagorean Theorem to solve for the length of the hypotenuse, or the original diagonal line.  

7.4.2 Find the Perimeter of a figure on a coordinate plane 

Example1: 

One day, Kelly left from home to the store to buy watercolors. She then went to school from stores. After the school, she walked through the direct path to home. Can you find the total distance Kelly covered on that day?  

Solution: 

To find the total distance, we need to find the perimeter of the triangles, which has the school, home and stores as coordinates.  

Step 1: Use absolute values to find the distances. 

Step 2: Find the length of the hypotenuse i.e., distance between school and home. 

The distance from school to home is 10 blocks. 

Step 3: Add all the three distances to find the total distance 

6 + 8 + 10 

= 24 

7.4.3 Use the Pythagorean Theorem to solve problems on the coordinate plane 

Example 1: 

Judy wats to draw an equilateral triangle on the coordinate plane. She drew one side of the triangle with vertices (3, 2) and (9, 2). She wants to draw the third vertex in the first quadrant. Can you help Judy with the coordinates of third vertex?  

Solution: 

Step 1: Find the length of the side drawn by Judy on a coordinate plane. 

Step 2: Use the Pythagorean Theorem to find the height of Judy’s triangle to the nearest tenth. 

Step 3: Complete the triangle by drawing the height to locate and label the third vertex. 

Exercise:

1. Use the Pythagorean Theorem to find the distance between points P1 and P2

• Use the Pythagorean Theorem to find the distance between points P1 and P2

• Use the Pythagorean Theorem to find the distance between points P1 and P2

• Points C and D represent the location of two parks on a map. Find the distance between the parks if the length of each unit on the grid is equal to 25 miles. Round to the nearest mile.

• One day Juan went out of his house and visited various places. The grid shows the path Juan followed when he walked from his home at (0, 0) to various locations and back home again. If each grid square represents one block, how many blocks did he walk?

• Find the perimeter of triangle ABC. Round the value to the nearest tenth.

• Find the perimeter of triangle ABC. Round the value to the nearest tenth.

• Find the perimeter of triangle ABC. Round the value to the nearest tenth.

• Triangle JKL is an equilateral triangle with two of its vertices at points J and K. What are the coordinates of point L? Round to the nearest tenth as needed

• Triangle JKL is an equilateral triangle with two of its vertices at points J and K. What are the coordinates of point L? Round to the nearest tenth as needed.

Concept Map :