Find a single matrix for the transformation that isequivalent to doing the following four transformationsof the plane in succession:1. Shear by a factor of 7 in the x-direction.2. Reflection over the line y = x.3. Expand by a factor of 5 in the y-direction.4. Rotate counter-clockwise by 90 degrees.Check Answer

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Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter2: Parallel Lines

Section2.CT: Test

Problem 11CT

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Find a single matrix for the transformation that is equivalent to doing the following four transformations of the plane in succession: 1. Shear by a factor of 5 in the x-direction. 2. Reflection over the line y = x. 3. Expand by a factor of 3 in the y-direction. 4. Rotate counter-clockwise by 90 degrees.
Find a single matrix for the transformation that is equivalent to doing the following four transformations of the plane in succession: 1. Shear by a factor of 2 in the x-direction. 2. Reflection over the line y=x. 3. Expand by a factor of 7 in the y-direction. 4. Rotate counter-clockwise by 90 degrees.
4. Do the following transformations on the rectangle shown in figure below in sequence. a. Shear the rectangle about y axis by shy =2. Using Shear Matrix and Equation b. After Change the position of the rectangle by a vector(2,3). c. Perform operation i) and i) for the rectangle by finding its Composite Matrix. Y axis 6. (1,4) (4,4) 4 (1,2) (4,2) Хаxis 1 4 5. An object is in location (1,3), (1,6), (3,3) and (3,6). Do two repeated translation operations on the object with the scaling factors, (2,1) and (4,3). Write the new positions. 6. An object is in location (0,0), (1,0), (0,1) and (1,1). Write the new positions after shearing the object about x-direction. Take shear parameter along x-direction shx=4.Then apply reflection about the line x=0(the Y axis). 7. Write tests performed on the vertices of polygon edges by Sutherland Hodgeman Polygon Clipping algorithm. Apply Left, Right, Bottom and Top boundary clipping in the following polygon as is done by Sutherland Hodgeman Polygon…
Find 1// (5x + 3y)dA where R is the parallelogram with vertices (0,0), (4,1), (5,3), and (9,4). Use the transformation x = 4и + 50, у %3 и + 3v .
Find the Jacobian of the transformation = 2u + 7v, y=u² - 5v.
Find ∫∫R(5x+2y)dA where R is the parallelogram with vertices (0,0), (-2,-4), (1,3), and (-1,-1).Use the transformation x=−2u+v, y=−4u+3v
Find (3x + 2y)dA where R is the parallelogram with vertices (0,0), (4,-4), (3,2), and (7,-2). R Use the transformation x = 4u + 3v, y - 4u + 2v
Find (2x + 3y)dA where Ris the parallelogram with vertices (0,0), (-5,-1), (1,-2), and (-4,-3). R Use the transformation x = 5u + v, y = – U – 2
Write down the 2 × 2 matrices that represent the following linear transformations ofthe plane. Also draw the image of the (first quadrant) unit square 1 under each transformation.(a) A dilation with horizontal dilation factor 2 and vertical dilation factor 1/2.(b) A vertical shear with factor −1/2. (c) A rotation of 450 anticlockwise. (d) A reflection across the line at angle −300 to the X-axis. (e) The transformation T(x, y) = (2x + 6y, x + 3y).
Find W (5x + 3y)dA where R is the parallelogram with vertices (0,0), (-1,-4), (-2,1), and (-3,-3). Use the transformation z = - u Give the exact answer. > Next Question -u-2v, y = - 4u+v
(3x + 2y)dA where R is the parallelogram with vertices (0,0), (3,-1), (4,-4), and R Find (7,-5). Use the transformation x = 3u +4v, y = u 4v.
Find (4x + 5y)dA where Ris the parallelogram with vertices (0,0), (-3,-5), (-1,-4), and (-4,-9). Use the transformation x = -3u v, y = -5u-4v

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