Question

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 A^I B^I C^I ? Plot ABC and A^I B^I C^I  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 A^II B^II C^II 
3. If A^II B^II C^II  is the image of ABC under transformation given by the matrix  . Find the coordinates of A^II B^II C^II. Plot A^II B^II C^II and describe the transformation fully. 

Answer 1

1. 
   
   
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 A^IB^IC^I = 1 x 6= 6 square units
3. 
   
   A^II (-3,2)  B^II (0,1) C^II(-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)