CK-12 Geometry-Concepts

7.12. Dilation in the Coordinate Plane http://www.ck12.org

2.A(− 4 , 6 ),k= 2

3.A( 9 ,− 13 ),k=^12

Answers

Remember that the mapping will be(x,y)→(kx,ky).

1.A′( 2 , 6 )

2.A′(− 8 , 12 )

3.A′( 4. 5 ,− 6. 5 )

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GivenAandA′, find the scale factor. You may assume the center of dilation is the origin.

1.A( 8 , 2 ),A′( 12 , 3 )

2.A(− 5 ,− 9 ),A′(− 45 ,− 81 )

3.A( 22 ,− 7 ),A′( 11 ,− 3. 5 )

The origin is the center of dilation. Find the coordinates of the dilation of each figure, given the scale factor.

4.A( 2 , 4 ),B(− 3 , 7 ),C(− 1 ,− 2 );k= 3

5.A( 12 , 8 ),B(− 4 ,− 16 ),C( 0 , 10 );k=^34

Multi-Step ProblemQuestions 6-12 build upon each other.

6. PlotA( 1 , 2 ),B( 12 , 4 ),C( 10 , 10 ). Connect to form a triangle.


7. Make the origin the center of dilation. Draw 4 rays from the origin to each point from #6. Then, plot
   A′( 2 , 4 ),B′( 24 , 8 ),C′( 20 , 20 ). What is the scale factor?


8. Usek=4, to findA′′B′′C′′. Plot these points.


9. What is the scale factor fromA′B′C′toA′′B′′C′′?


10. Find (Ois the origin):
    a.OA
    b.AA′
    c.AA′′
    d.OA′
    e.OA′′


11. Find:
    a.AB
    b.A′B′
    c.A′′B′′


12. Compare the ratios:
    a.OA:OA′andAB:A′B′
    b.OA:OA′′andAB:A′′B′′

For questions 13-18, use quadrilateralABCDwithA( 1 , 5 ),B( 2 , 6 ),C( 3 , 3 )andD( 1 , 3 )and its transformationA′B′C′D′
withA′(− 3 , 1 ),B′( 0 , 4 ),C′( 3 ,− 5 )andD′(− 3 ,− 5 ).

13. Plot the two quadrilaterals in the coordinate plane.


14. Find the equation of

←→

CC′.