Answer: Let the columns of 2 4 3 4 ~] be the homogeneous fonn of the coordinates of the

Chapter 6, Problem 3

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Let the columns of 2 4 3 4 ~] be the homogeneous fonn of the coordinates of the vertices of a triangle in the plane. Note that the first and last columns are the same. indicating that the figure is a closed region. (a) In a coordinate plane. sketch the triangle determined by S. Connect its vertices with straight line segments. (b ) The triangle determined by S is 10 be rotated by 30' counterclockwise and then rotated again by 90' counterclockwise. Detennine the 3 x 3 matrix M in homogeneous form that represents the composite transformation or these two rotations. (c) Use the matrix M from part (b) to determine the image of the triangle and sketch it in a coordinate plane. (d) Determine the matrix Q in homogeneous form that would first perfonn the rotation through 90' followed by the rotation through 30. (e) Use the matrix Q from part (d) to determine the image of the triangle and sketch it in a coordinate plane. (I) Are the images from parts (c) and (e) the same? Explain why or why not.