Worksheet: Linear Transformations in Planes: Scaling

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 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 the origin
  • Ba dilation with scale factor 3 and center 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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