CK12 - Geometry

DistanceFormula: Givepoints and , the lengthof the segmentcon-

nectingthosetwo pointsis

Example 6

Use the distanceformula to find the distancebetweenthe points(1,5)
and (5,2) on a coordinategrid.

You alreadyknowfrom example1 that the distancewill be units,but you can practiceusingthe distance

formulato makesure it works.In this formula,substitute for , for , for , and for because

and are the two pointsin question.

Now you see that no matterwhichmethodyou use to solvethis problem,the distancebetween and

on a coordinategrid is units.

LessonSummary

In this lesson,we exploredhow to workwith differentradicalexpressionsboth in theoryand in practicalsit-
uations.Specifically, we havelearned:

• How to identifyand employthe PythagoreanTheoremwhenworkingwith right triangles.


• How to identifycommonPythagoreantriples.


• How to use the PythagoreanTheoremto find the area of isoscelestriangles.


• How to use the PythagoreanTheoremto derivethe distanceformulaon a coordinategrid.

Theseskillswill help you solvemanydifferenttypesof problems.Alwaysbe on the lookoutfor new and in-
terestingwaysto applythe PythagoreanTheoremto mathematicalsituations.

Pointsto Consider

Now that you havelearnedthe PythagoreanTheorem,thereare countlesswaysto applyit. Couldyou use
the PythagoreanTheoremto provethat a trianglecontaineda right angleif you did not havean accurate
diagram?

LessonExercises

1. Whatis the distancebetween and?


2. Do the numbers , , and makea Pythagoreantriple?