The 3x3 matrix that produces the composite 2Dtransformation that rotates points through 45° aboutthe point (7,4) using homogeneous coordinates isshown to the right. Show that this transformation isequivalent to a rotation about the origin followed bya translation by p. Find p.3/27-211 /24 -0 01This is equivalent to a rotation through oabout the origin, followed by a translation by p=

The 3 × 3 matrix for a rotation about the origin at an angle θ is given by Rθ=cosθ−sinθ0sinθcosθ0001…

Answered: The 3x3 matrix that produces the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 39E

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Find the Jacobian of the transformation = 2u + 7v, y=u² - 5v.
Write down the 4 by 4 matrix S that scales by a constant c. Multiply ST and also TS, where T is translation by (1, 4, 3). To blow up the picture around the center point (1, 4, 3), would you use vST or vT S?
REFER TO IMAGE
Plot the following coordinates: A (3, 2), B (4, 5) and C (2, 5). Connect the points to form triangle ABC. Find the 3 by 3 matrix that corresponds to the composite transformation of, a rotation of 45 degrees about the origin, a scaling by 0.6 and finally a translation that adds (4, 6) to each point of a figure. Plot the final vertices.
Which of the following describes 2D rotation? OxformMatrix.rotate(0, 1, 0, 0); OxformMatrix.rotate(1, 0, 1, 0); OxformMatrix.rotate(1, 0, 0, 1); OxformMatrix.rotate(0, 0, 1, 0);
The point M is (2,5) and the point N is (-3,-1). The line segment MN is transformed to the line segment TU by two transformations: MN is rotated 90° clockwise about the origin to give the line segment RS. RS is then translated by the vector to give the line segment TU. The coordinates of the midpoint of TU are (7,–2.5). Find the vector 2 A 0.5 0.5 B -3 3 D 5 9. 2 LO
A triangle is defined by the coordinates P1(3, 0, 0), P2(0, 5, 0) and P3(0, 0, 7). The triangle is rotated 30-degree counter-clockwise about the x-axis. Solve the transformation operation to determine the new position of the triangle (a) (b) The rotated triangle in (a) is next rotated 45-degree counter-clockwise about the z-axis. Solve the transformation operation to determine the new position of the triangle. (c) Instead of the rotations in (a) and (b), the original triangle in (a) at coordinate P:(3, 0, 0), P2(0, 5, 0) and P3(0, 0, 7) is now rotated 30-degree clockwise about the x-axis. Next, the rotated triangle is then rotated 45-degree clockwise about the z-axis. Solve the transformation operation to determine the final position of the triangle. (d) Explain how you can rotate the rotated triangle in part (b) to its original position at P:(3, 0, 0), P2(0, 5, 0) and P3(0, 0, 7).

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The 3x3 matrix that produces the composite 2D transformation that rotates points through 45° about the point (7,4) using homogeneous coordinates is shown to the right. Show that this transformation is equivalent to a rotation about the origin followed by a translation by p. Find p.