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.

11 , yx

22 , yx

Form a right triangle

11 , yx

22 , yx

Using Pythagorean Theorem let’s find the distance formula

Pythagorean Theorem Set up to solve for our segment, c Use the Symmetric Property

222 cba

222 bac

Define the Variables Of

Pythagorean Theorem

Let a be the altitude, yLet b be the base, x

andLet c be the distance, d

21 yya

21 xxb dc

21 yya

21 xxb 22 , yx

11, yx

dc

Substitution

222 bac

2212

212 xxyyd

becomes

Take the Square Root both sides What do you get?

2212

21 yyxxd

Let’s Try it with numbers!Let (x1,y1) and (x2,y2)

be (2,3) and (5,8)

Substitute into the distance formula

2212

21 yyxxd

Substituted

Simplified, order of operation

22 8352 d

22 53 d

259 d

34d

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