The Distance Formula

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

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

Form a right triangle

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

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

Substitution becomes

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

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

 Substituted  Simplified, order of operation

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