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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 10RE

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Question

Find the coordinates of the vertices of each figure after the given transformation.
rotation 180° about the origin
A y:
R
O T(-2,0), S'(-5,1), R'(-4, 3), Q'(0, 4)
O T(0, -2), S'(-1, –5), R'(-3, –4), Q'(-4,0)
O S'(1, –3), R'(3, -2), Q'(4, 2), T'(0, 0)
O S(1, –5), R'(3, -4), Q'(4,0), T"(0,-2)
9 10

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For the linear transformation from Exercise 45, let =45 and find the preimage of v=(1,1). 45. Let T be a linear transformation from R2 into R2 such that T(x,y)=(xcosysin,xsin+ycos). Find a T(4,4) for =45, b T(4,4) for =30, and c T(5,0) for =120.
A translation in R2 is a function of the form T(x,y)=(xh,yk), where at least one of the constants h and k is nonzero. (a) Show that a translation in R2 is not a linear transformation. (b) For the translation T(x,y)=(x2,y+1), determine the images of (0,0,),(2,1), and (5,4). (c) Show that a translation in R2 has no fixed points.
Let T:P2P3 be the linear transformation T(p)=xp. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3}.
Let T:P2P4 be the linear transformation T(p)=x2p. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3,x4}.
Sketch the image of the unit square [a square with vertices at (0, 0), (1, 0), (1, 1), and (0, 1)] under the specified transformation.T is a reflection in the line y = x.
Sketch the image of a unit square [a square with vertices at (0, 0), (1, 0), (1, 1), and (0, 1)] under the specified transformation. T is a reflection in the line y = −x.
Apply the transformation T (x, y) = (0.8x − 0.6y, 0.6x + 0.8y) to the scalene triangle whose vertices are (0, 0), (5, 0), and (0, 10). What kind of isometry does T seem to be? Be as specific as you can, and provide numerical evidence for your conclusion.
Find the Jacobian ∂(x,y,z)/∂(u,v,w) of the transformations below.
Suppose S is the unit square in the first quadrant of the uv-plane.Describe the image of the transformation T: x = 2u, y = 2v.
Use the rule (x, y) → (3x, 2y) to find the image for the preimage defined by thepoints. Determine whether the transformation is a rigid motion. 4. A(3, 5) , B(5, 3) , C(2, 2) How would I be able to work this step by step?
The following coordinates are a result of a single transformation. What type of transformation occurred for image C'?
Sketch the image of the triangle with vertices (0, 0), (1, 0), and (0, 1) under the specified transformation.T is a reflection in the x-axis.

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