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Worksheet: Properties of Linear Transformations


Consider the matrix where .

Find .

  • A
  • B
  • C
  • D
  • E

Find .

  • A0
  • B2
  • C
  • D
  • E1

By drawing the image of the unit square under the transformation, identify the geometrical transformation this matrix corresponds to.

  • Aa rotation by clockwise about the origin about the point
  • Ba reflection in the line
  • Ca reflection in the line
  • Da projection onto the line
  • Ea rotation of clockwise about the origin


Consider the transformation represented by the matrix

What is the image of the square with vertices , , , and under this transformation?

  • Aa kite with vertices , and
  • Ban arrowhead with vertices , and
  • Ca square with vertices , , , and
  • Dan arrowhead with vertices , and
  • Ea square with vertices , , , and

What geometric transformation does this matrix represent?

  • Aa rotation about the origin by an angle of
  • Ba stretch in the -direction
  • Ca dilation with scale factor and center the origin
  • Da stretch in the -direction
  • Ea dilation with scale factor 3 and center the origin


The vertex matrix of a square of side 1 shown is

Determine the vertex matrix of the image after a transformation by the matrix , and state what geometric figure it is.

  • A, a parallelogram
  • B, a rhombus
  • C, a square
  • D, a rectangle