CK12 - Geometry

To find the imageof , we can applythe sametransformationvectorto point. The arrowheadof the

vectoris at.

The vectorin example2 is oftenrepresentedwith a boldfacesingleletterv.

• The horizontalcomponentof vector is.


• The verticalcomponentof vector is.


• The vectorcan also be representedas a numberpair madeup of the horizontaland verticalcomponents.

The vectorfor this transformationis

Example 3

A trianglehas vertices , , and. The vectorfor a translationis

. Whatare the verticesof the imageof the triangle?

Add the horizontaland verticalcomponentsto the - and -coordinatesof the vertices.

Challenge:Can you describewhatthis transformationdoesto the originaltriangle?

FurtherReading

Vectorsare usedin physicsto representforces,velocity, and otherquantities.Learnmoreaboutvectors
at:

http://en.wikipedia.org/wiki/Vector_(spatial)

LessonSummary

You can thinkof a translationas a way to movepointsin a coordinateplane.And you can be sure that the
shapeand size of a figurestaysthe samein a translation.For that reasona translationis calledanisometry.
(Note:Isometryis a compoundwordwith two rootsin Greek,“iso” and “metry.” You may knowotherwords
with thesesameroots,in additionto “isosceles”and “geometry.”)

Vectorsprovidean alternativeway to representa translation.A vectorhas a directionand a length—the
exactfeaturesthat are involvedin movinga pointin a translation.

Pointsto Consider

Thinkaboutsomespecialtransformationvectors.Can you picturewhateachone doesto a figurein a coor-
dinateplane?

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