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

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 aclosed region.(a) In a coordinate plane. sketch the triangle determinedby S. Connect its vertices with straight line segments.(b ) The triangle determined by S is 10 be rotated by30' counterclockwise and then rotated again by 90'counterclockwise. Detennine the 3 x 3 matrix Min homogeneous form that represents the compositetransformation or these two rotations.(c) Use the matrix M from part (b) to determine theimage of the triangle and sketch it in a coordinateplane.(d) Determine the matrix Q in homogeneous form thatwould first perfonn the rotation through 90' followedby the rotation through 30.(e) Use the matrix Q from part (d) to determine theimage of the triangle and sketch it in a coordinateplane.(I) Are the images from parts (c) and (e) the same? Explainwhy or why not.

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