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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 29E
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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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