1. The Distance Formula Chapter 1.8

2. Practicing Skills We Know… • On your graph paper, Plot and label point A at (2,1), point B at (6, 4) and point C(6,1). Connect the points to form a right triangle.

3. Practicing Skills We Know… B(6,4) A(2,1) C(6,1)

4. Practicing Skills We Know… • Using the grid, Find the lengths of segments BC and CA. These are the legs of triangle ABC.

5. Practicing Skills We Know… B(6,4) A(2,1) C(6,1)

6. Practicing Skills We Know… • Use the Pythagorean theorem to find the length AB. AB is the hypotenuse of triangle ABC.

7. Practicing Skills We Know… B(6,4) A(2,1) C(6,1)

8. Deriving the Distance Formula • The steps we just practiced can be used to derive the general formula for the distance between two points on the coordinate plane. • For this formula, the coordinates of point A will be at (x1, y1) and point B will be at (x2, y2)

9. Deriving the Distance Formula What are the coordinates of C?

10. Deriving the Distance Formula What are the lengths of the triangle’s legs? AC = x2 – x1 BC = y2 – y1

11. Deriving the Distance Formula What is the length of the triangle’s hypotenuse?

12. The Distance Formula • Used to find the distance between two points

13. The Distance Formula • Example: Find the distance between A(4,8) and B(1,12) A (4, 8) B (1, 12)