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Lesson Worksheet: Linear Transformations in Planes: Scaling Mathematics • 10th Grade

In this worksheet, we will practice finding the matrix that scales a vector by a given scaling factor and the image of the vector under scaling linear transformation.

Q1:

Consider the transformation represented by the matrix 3003.

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

  • AA kite with vertices (0,0),(1,3),(3,1), and (3,3)
  • BA kite with vertices (0,0),(0,1),(1,0), and (3,3)
  • CA square with vertices (0,0), (0,1), (1,0), and (3,3)
  • DA square with vertices (0,0), (0,1), (1,0), and (1,1)
  • EA square with vertices (0,0), (0,3), (3,0), and (3,3)

What geometric transformation does this matrix represent?

  • AA stretch in the 𝑦-direction
  • BA stretch in the 𝑥-direction
  • CA rotation about the origin by an angle of 3
  • DA dilation with scale factor 3 and center at the origin
  • EA dilation by a factor of 3 with its center at the point (1,1)

Q2:

Consider the transformation represented by the matrix 3003.

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)
  • BAn arrowhead with vertices (0,0),(0,3),(3,0), and (3,3)
  • CA kite with vertices (0,0),(0,1),(1,0), and (3,3)
  • DAn arrowhead with vertices (0,0),(0,3),(3,0), and (3,3)
  • EA square with vertices (0,0), (0,3), (3,0), and (3,3)

What geometric transformation does this matrix represent?

  • AA dilation with scale factor 3 and center at the origin
  • BA dilation with scale factor 3 and center at the origin
  • CA stretch in the 𝑦-direction
  • DA stretch in the 𝑥-direction
  • EA rotation about the origin by an angle of 3

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