the distance formula the distance formula is used to find the length of the segment
TRANSCRIPT
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