Answer just #2 please proof 9:45 1LTEA aproged.ptpositions of the circle meet at B and C, these are two vertices of thedesired rectangle ABCD, whose sides AB and DC are equal andparallel to a.82TRANSFORMATIONSFigure 4.1DEXERCISES1. In AABC (Figure 4.1E) “inscribe" a line segment equal and parallelto the given segment a.2. Draw a figure to illustrate part of the infinite pattern that can be derivedfrom a given equilateral triangle ABC by applying all the vectors con-sisting of an integral multiple of AB plus an integral multiple of AC.Figure 4.1E4.2 RotationAnother kind of transformation that preserves distance is rotation.Here the entire plane is turned about some point through a given angle.Thus the size and shape of any figure are kept invariant, but its pointsall move along arcs of concentric circles. The center (which may ormay not “belong" to the figure being rotated) is the only point thatremains fixed.As an example of the use of a rotation, let us consider AABC (Figure4.2A) with equilateral triangles BPC, CQA, ARB erected (externally)on the three sides. After drawing the lines BQ and Cr, which meet atF, we observe that a rotation through 60° about A takes AARC intoAA BQ. Hence ZRFB = 60° and RC = BQ. Similar reasoningshows that PA = CR. ThusAP = BQ = CR.ROTATION83Moreover, sinceZRFB = 60° = ZRAB and 2CFQ = 60° = 2CAQ,the quadrangles A RBF and CQAF are cyclic; and since ZBFC = 120°while 2CPB = 60 PEPidrangle. Therefore the

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Description: Answer just #2 please proof 9:45 1LTEA aproged.ptpositions of the circle meet at B and C, these are two vertices of thedesired rectangle ABCD, whose sides AB and DC are equal andparallel to a.82TRANSFORMATIONSFigure 4.1DEXERCISES1. In AABC (Figure 4.

Given data is: Draw a figure to illustrate the part of infinite pattern that can derived from…

Math

Geometry

2. Draw a figure to illustrate part of the infinite pattern that can be derived from a given equilateral triangle ABC by applying all the vectors con- sisting of an integral multiple of AB plus an integral multiple of AC.

2. Draw a figure to illustrate part of the infinite pattern that can be derived from a given equilateral triangle ABC by applying all the vectors con- sisting of an integral multiple of AB plus an integral multiple of AC.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.2: Length And Angle: The Dot Product

Problem 6AEXP

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