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The triangle ABC has vertices A (1, 2), B (2, 1) and C (2, 3). AI BI CI is the image of ABC under transformation given by the matrix

  1. What are the coordinates of ABI C? Plot ABC and AI BI CI  on the same axis 
  2. State the ratio of the areas of the two triangles and use the area of ABC to calculate the area of AII BII CII 
  3. If AII BII CII  is the image of ABC under transformation given by the matrix sukmathsp220c . Find the coordinates of AII BII CII. Plot AII BII CII and describe the transformation fully. 

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  1. sukmathsp2ans20a
  2. Ratio of the 2 triangles = determinant of matrix
     (2 x 3) = (0 x 0) =6
    thus ratio = 6:1
    Area of ABC = ½ x 2 x 1= 1 square unit
    Area of AIBICI = 1 x 6= 6 square units

  3. sukmathsp2ans20c
    AII (-3,2)  BII (0,1) CII(-4,3)
    The transformation is a shear parallel to the x axis with the x axis invariant shear factor. The image of A(1,2) is A1(-3,2)

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