1. Find the image of the point (2, 3) under the following matrices.
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a.
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b.
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c.
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2. a. Sketch a triangle ABC such that:
A = (4, 3)
B = (1, 1)
C = (3, 0)
b. Multiply each point by the matrix M =
c. Sketch each image point on the diagram.
d. What transformation maps Δ ABC to Δ A'B'C'?
3. Sketch a square PQRS such that:
P = (1, 1), Q = (1, -1), R = (-1, 1) and S = (-1, -1)
b. Multiply each point by the matrix N =
to find P'Q'R'S'.
c. Sketch each point on the diagram.
d. What transformation maps PQRS to P'Q'R'S'?e. Evaluate the ratio Area of P'Q'R'S':Area of PQRS.
f. Is the answer to part e equal to the determinant of N
4. For each of the following transformation matrices, draw a unit square and find its image. Describe each transformation fully.
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a.
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b.
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c.
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d.
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e.
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f.
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g.
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h.
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5. a. Transform the triangle ABC by the matrix M = , where A = (1, 1), B = (3, 1) and C = (3, 3). Label the image A'B'C'.
b. Find the area of triangles ABC and A'B'C'.
c. Calculate the determinant of matrix M.
