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Lesson: Dilation Transformation Matrix

Sample Question Videos

Worksheet • 5 Questions • 1 Video

Q1:

Consider the transformation represented by the matrix  3 0 0 3  .

What is the image of the square with vertices ( 0 , 0 ) , ( 0 , 1 ) , ( 1 , 0 ) , and ( 1 , 1 ) under this transformation?

  • Aa square with vertices ( 0 , 0 ) , ( 0 , 3 ) , ( 3 , 0 ) , and ( 3 , 3 )
  • Ba square with vertices ( 0 , 0 ) , ( 0 , 1 ) , ( 1 , 0 ) , and ( 3 , 3 )
  • Ca kite with vertices ( 0 , 0 ) , ( 1 , 3 ) , ( 3 , 1 ) , and ( 3 , 3 )
  • Da square with vertices ( 0 , 0 ) , ( 0 , 1 ) , ( 1 , 0 ) , and ( 1 , 1 )
  • Ea kite with vertices ( 0 , 0 ) , ( 0 , 1 ) , ( 1 , 0 ) , and ( 3 , 3 )

What geometric transformation does this matrix represent?

  • Aa dilation with scale factor 3 and center the origin
  • Ba dilation by a factor of 3 with its center at the point ( 1 , 1 )
  • Ca stretch in the π‘₯ -direction
  • Da rotation about the origin by an angle of 3 ∘
  • Ea stretch in the 𝑦 -direction

Q2:

Describe the geometric effect of the transformation produced by the matrix  0 βˆ’ 3 3 0  .

  • Aa dilation with center the origin and scale factor 3 followed by a 9 0 ∘ rotation about the origin
  • Ba dilation with center the origin and scale factor 3 followed by a 1 8 0 ∘ rotation about the origin
  • Ca dilation with center the origin and scale factor 3 followed by a reflection in the line 𝑦 = π‘₯
  • Da dilation with center the origin and scale factor 3 followed by a reflection in the line 𝑦 = βˆ’ π‘₯
  • Ea dilation with center the origin and scale factor 3 followed by a βˆ’ 9 0 ∘ rotation about the origin

Q3:

A dilation with center the origin is composed with a rotation about the origin to form a new linear transformation. The transformation formed sends the vector  3 4  to  βˆ’ 3 3 5 6  .

Find the matrix representation of the transformation formed.

  • A  5 βˆ’ 1 2 1 2 5 
  • B  5 1 2 1 2 5 
  • C  5 βˆ’ 1 2 1 2 5 
  • D  βˆ’ 1 2 . 9 2 1 . 4 4 1 . 4 4 1 2 . 9 2 
  • E  βˆ’ 1 1 0 0 1 4 

Find the scale factor of the original dilation.

  • Ascale factor = 13
  • Bscale factor = 13
  • Cscale factor = 169
  • Dscale factor = √ 1 1 9
  • Escale factor = 154
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