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Consider the (x, y) vertices of an equilateral triangle in R² given by, (0,0), (1,0), (.5, √3/2) Perform the following actions in order using matrix transformations: (a) Reflect the triangle over the x-axis, (b) Compress the triangle along the y-axis by a factor of 2, (c) Rotate the triangle counterclockwise by π/6 radians about the origin, and (d) Shear the triangle along the x-axis by a factor of 0.5. Clearly show the matrix transformations used and compute the final set of vertices of the triangle.

Consider the (x, y) vertices of an equilateral triangle in R² given by, (0,0), (1,0), (.5, √3/2) Perform the following actions in order using matrix transformations: (a) Reflect the triangle over the x-axis, (b) Compress the triangle along the y-axis by a factor of 2, (c) Rotate the triangle counterclockwise by π/6 radians about the origin, and (d) Shear the triangle along the x-axis by a factor of 0.5. Clearly show the matrix transformations used and compute the final set of vertices of the triangle.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the (x, y) vertices of an equilateral triangle in R² given by, (0,0), (1,0), (.5, √3/2) Perform the following actions in order using matrix transformations: (a) Reflect the triangle over the x-axis, (b) Compress the triangle along the y-axis by a factor of 2, (c) Rotate the triangle counterclockwise by π/6 radians about the origin, and (d) Shear the triangle along the x-axis by a factor of 0.5. Clearly show the matrix transformations used and compute the final set of vertices of the triangle.
Transcribed Image Text:Consider the (x, y) vertices of an equilateral triangle in R² given by, (0,0), (1,0), (.5, √3/2) Perform the following actions in order using matrix transformations: (a) Reflect the triangle over the x-axis, (b) Compress the triangle along the y-axis by a factor of 2, (c) Rotate the triangle counterclockwise by π/6 radians about the origin, and (d) Shear the triangle along the x-axis by a factor of 0.5. Clearly show the matrix transformations used and compute the final set of vertices of the triangle.
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