This document provides instruction on using the Pythagorean theorem and distance formula to calculate the distance between two points. It explains that you need to know the coordinates of the two points, then find the difference between their x- and y-values to get the legs of a right triangle. You square each leg value, add them, and take the square root of the sum to find the hypotenuse, which represents the distance between the points. Examples are given to demonstrate how to set up and solve problems using this method.

1. Bellwork
• Find quiz and start corrections
SILENTLY
• Take out homework from last night
• Take out blank paper for notes

2. Find the exact distance between A and B

3. Create a Right Triangle to find the distance
Now you can use the Pythagorean Theorem
to solve the length of AB

4. Or we can rewrite the Pythagorean
Theorem

5. What do you need to know
to solve the Pythagorean
Theorem?
The length of Leg 1
The length of Leg 2

6. How would you find the
length of Leg 1?
(10, 5)
Count the squares
OR
Subtract the Y coordinates
(2,1)
5 – 1 = 4
4

7. How would you find the
length of Leg 2?
Count the squares
OR
(10, 5)
Subtract the X coordinates
(2,1)
10 – 2 = 8
8

8. Finding the length of the Hypotenuse
• The Pythagorean Theorem says
a2 + b2 = c2
• In this case a is the same as subtracting the Y coordinates
or (y1 – y2)
• In this case b is the same as subtracting the X coordinates
or (x1 – x2)
• And since the Pythagorean Theorem says you have to square
a and b and then add them
(y1 – y2)2 + (x1 – x2)2 = c2

9. Distance Formula
(y1 – y2)2 + (x1 – x2)2 = c2
In the end you have to take the
square root of the final answer…

10. Using the Distance Formula…
• Find the length of AB