2. The Distance Formula

3. The distance formula is used to find the Length of the segment

4. Let’s look at the segment without the grid Now let’s label the endpoints, using a general notations for a grid.

5. Form a right triangle

6. Using Pythagorean Theorem let’s find the distance formula  Pythagorean Theorem  Set up to solve for our segment, c  Use the Symmetric Property

7. Define the Variables Of Pythagorean Theorem Let a be the altitude, y Let b be the base, x and Let c be the distance, d

10. Substitution becomes

11.  Take the Square Root both sides  What do you get?

12. Let’s Try it with numbers! Let (x 1,y 1 ) and (x 2,y 2 ) be (2,3) and (5,8) Substitute into the distance formula

13.  Substituted  Simplified, order of operation

14. When do we use this? Distance formula is used to find a length of a segment on a Cartesian Plane. We will use this in conjunction with slope to prove or to disprove a quadrilateral is a square, rectangle, parallelogram or a rhombus. We may also use it to prove or disprove that a triangle is equilateral or isosceles. The End