CK12 - Geometry

Note:The distancefrom the originto is WhenP rotates its imageis on the -axis,the

samedistancefrom the originas.

LessonSummary

To find , the imageof polygonmatrix rotatedaboutthe origin:

1. Rotation


2. Rotation


3. Rotation

Pointsto Consider

You’venow studiedseveraltransformationsthat are isometries:translations,reflections,and rotations.Yet
to comeis one morebasictransformationthat isnotan isometry, whichis the dilation.

The LessonSummaryabovelisteda few formulasfor rotations.Supposeyou only had the first two formulas.

Would you be able to find the coordinatesof the imageof a polygonthat rotates or or

For that matter, wouldformula2 in the summarybe enoughto find the imageof a polygonthat rotates
Theserotationscan be solvedusingcompositionsof otherrotations,a topiccomingup in a later lesson.

LessonExercises

Let be the pointwith coordinates.

1. Write a matrix to representthe coordinatesof


2. Write the matrixfor the product


3. Whatare the coordinatesof the point representedby the product?


4. Provethat , the origin , and are collinear.


5. Provethat