Name:_______________________________________________ Date:____________________ Period:_________ Pythagorean Theorem and Distance Formula In the following activity, you will discover the Distance Formula. Do you remember the Pythagorean Theorem?? _____________________________ First, let’s look at some segments that are drawn in the coordinate plane. 1. How could you find the length of AB ? Explain the process you used. 2. How could you find the length of CD ? Explain the process you used. 3. How could you find the length of EF ? Explain the process you used. 4. Is it easier to find the length of AB or EF ? Explain your answer. 5. Some of you may have chosen to find the length of EF by using the Pythagorean Theorem. When you used the Pythagorean Theorem, what did you do to find the values for a and b? Did you have to draw anything else on the graph? 6. Write an algebraic equation that shows how you arrived at the value for a and the value for b. 7. Use these equations plus the Pythagorean Theorem to write a new equation. 8. What does c represent? 9. Solve the equation for c. You have now derive the Distance Formula from the Pythagorean Theorem.