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A quiz question from a university-level linear algebra course, mathematics 205, during the fall semester 2004. The question asks students to perform several transformations on a triangle v in the plane with vertices (5, 0), (2, 2), and (4, 3). The tasks include sketching the triangle, converting it to homogeneous coordinates, reflecting it through the line x1 = x2, moving the reflected triangle, and sketching the image of the triangle under the transformation.
Typology: Exercises
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(^5) is the data matrix for a triangle V in the plane with vertices (5, 0), (2, 2), and (4, 3).
A. Sketch a graph of V.
B. Give a 3 x 3 data matrix for V using homogeneous coordinates.
C. Give a 3 x 3 matrix which first reflects V through the line x 1 = x (^2) then moves the reflected triangle one unit horizontally and two units vertically.
D. Sketch the image of V under this transformation.