2. (a) Let L be a set of points in the plane. Consider the following statement S:"If L is described by the equation y = mx + c for some m, c E R, then L is astraight line."(i) Is S true?(ii) Write down the converse of S.(iii) Is the converse of S true?Briefly explain your answers.(b) In each of the following situations find a formula describing the locus of the pointP, in Cartesian coordinates, and briefly describe the shape of the locus. (It is notnecessary to give detailed geometric properties of the shape such as its centre.)(i) The distance from P₁ to the point (-2,2) is equal to that from P₁ to (0,4).(ii) The distance from P₂ to the point (1,3) is twice that from P₂ to (-1,2).(iii) The distance from P3 to the line 3y = 4x is 1.(iv) The distance from P to the point (-5, 3) is twice the distance from P4 tothe line with equation 4x + 3y + 5 = 0.

a) Given the statement S: " If L is described by the equation y=mx+c foe some m, c∈ℝ, then L is a…

Answered: 2. (a) Let L be a set of points in the…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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2. (a) Let L be a set of points in the plane. Consider the following statement S: "If L is described by the equation y = mx + c for some m, c ER, then L is a straight line." (i) Is S true? (ii) Write down the converse of S. (iii) Is the converse of S true?