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(please note that these points are expressed in homogeneous coordinates). You want to uniformly scale point P₂ by 1/2 and then rotate point p₂ by 45 degrees. Though, you want to perform these two operations about point p₁, i.e., not the origin. After this transformation, the new 1 2+√2 location of the point p2 is p'2 : = a. Consider the two 2D points: P₁ = 1 and P₂ = b. C. 2 1 You will need four 3 × 3 transformation matrices to perform the above transformation. Clearly write the contents of each of these four matrices and indicate the name of the affine transformation for each. Entries in all matrices must have numeric values. Write the four transformation matrices in part (a) as a sequence of multiplications that would correctly perform the transformation. Add the point p2 to the matrix sequence in part (b) and complete the multiplication. Your final answer should be point p'2. Show the result of each matrix multiplication.

(please note that these points are expressed in homogeneous coordinates). You want to uniformly scale point P₂ by 1/2 and then rotate point p₂ by 45 degrees. Though, you want to perform these two operations about point p₁, i.e., not the origin. After this transformation, the new 1 2+√2 location of the point p2 is p'2 : = a. Consider the two 2D points: P₁ = 1 and P₂ = b. C. 2 1 You will need four 3 × 3 transformation matrices to perform the above transformation. Clearly write the contents of each of these four matrices and indicate the name of the affine transformation for each. Entries in all matrices must have numeric values. Write the four transformation matrices in part (a) as a sequence of multiplications that would correctly perform the transformation. Add the point p2 to the matrix sequence in part (b) and complete the multiplication. Your final answer should be point p'2. Show the result of each matrix multiplication.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 44E
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2) points are expressed in homogeneous coordinates). You want to uniformly scale point P2 by 1/2 and then rotate point p2 by 45 degrees. Though, you want to perform these two operations about point p₁, i.e., not the origin. After this transformation, the new 1 2+√2 location of the point p₂ is p'2 a. Consider the two 2D points: p₁ = 1 and P₂ -1- = b. C. = 121 2 (please note that these 2 1 You will need four 3 × 3 transformation matrices to perform the above transformation. Clearly write the contents of each of these four matrices and indicate the name of the affine transformation for each. Entries in all matrices must have numeric values. Write the four transformation matrices in part (a) as a sequence of multiplications that would correctly perform the transformation. Show Add the point p2 to the matrix sequence in part (b) and complete the multiplication. Your final answer should be point p'2. the result of each matrix multiplication.
Transcribed Image Text:2) points are expressed in homogeneous coordinates). You want to uniformly scale point P2 by 1/2 and then rotate point p2 by 45 degrees. Though, you want to perform these two operations about point p₁, i.e., not the origin. After this transformation, the new 1 2+√2 location of the point p₂ is p'2 a. Consider the two 2D points: p₁ = 1 and P₂ -1- = b. C. = 121 2 (please note that these 2 1 You will need four 3 × 3 transformation matrices to perform the above transformation. Clearly write the contents of each of these four matrices and indicate the name of the affine transformation for each. Entries in all matrices must have numeric values. Write the four transformation matrices in part (a) as a sequence of multiplications that would correctly perform the transformation. Show Add the point p2 to the matrix sequence in part (b) and complete the multiplication. Your final answer should be point p'2. the result of each matrix multiplication.
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