CK12 - Geometry

is , is is Eachrow in the matrixbelowrepresentsthe coordinatesof one of the vertices. In the translation,supposethat eachpointwi ...

The coordinatesof the imageof any point will be the point. The translationcan be representedas a matrixsum. Example 4 Whatis the ...

2. 3. Matrix belowrepresentsthe verticesof a triangle.How doesthe trianglemovein the translationrepre- sentedby matrix 4. 5. 6. ...

Matrix representsthe verticesof a triangle.How doesthe trianglemovein the translationrepresented by the matrixsum? 7. 8. 9. Wri ...

3. Doesnot move unitsright unitsleft and unitsdown unitsleft unitsup unitsleft and unitsup 11. 12. 13. ...

Reflections LearningObjectives Find the reflectionof a pointin a line on a coordinateplane. Multiplymatrices. Applymatrixmultip ...

Try this. Drawa line. Drawa triangle. Reflectthe trianglein the line. Lookat your results. Repeatwith differentlines,and figure ...

We now havethesereflectionsof : Reflectionof in the -axisis. [ -coordinatestaysthe same, -coordinatebecomesopposite] Reflecti ...

Finally, we can showthat is the perpendicularbisectorof. Midpointof is. Midpointof is on ( - and -coordinatesof are the same). ...

Conclusion:Whena segmentis reflectedin the -axis,the imagesegmenthas the samelengthas the originalsegment.This is the meaningof ...

To computea givenelementof the productmatrix,we multiplyeachelementof that row in the left matrix by the correspondingelementin ...

Now we can use matrixarithmeticto expressreflections. Givena point in the coordinateplane,we will use matrixmultiplicationto ref ...

The trapezoidbelowis reflectedin the line. Whatare the coordinatesof the verticesof the imageof the trapezoid? Write a polygonm ...

Multiplicationof a polygonmatrixby one of the specialmatrices , , or will reflect the polygonin the -axis,the -axis,or the line ...

3. 4. Let be a polygonmatrix.Fill in the blank(s). If , then ?. If , and is a -by- matrix,then is a -bymatrix. If , then ? If ...

Applymatrixmultiplicationto rotations. SampleRotations In this lessonwe limit our studyto rotationscenteredat the originof a c ...

Notice: and are the endpointsof a diameter. The rotationis the sameas a “reflectionin the origin.” A rotationis an isometry. The ...

In a rotation,the imageof is the point. Notice: and are radii of the samecircle,so. is a right angle. The acuteangleformedby and ...

If is a polygonmatrix,then the matrixfor the imageof the polygonin a rotationis the product . The LessonExercisesincludeexplorat ...

Rotationsin General Let be a polygonmatrix.The matrixfor the imageof the polygonin a rotationof degreesis the product , where Ex ...