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.m..Theorem 9.10bGivenLinesl1and l2with slope ProveProofChoose any point on mis k.EXAMPLE 1The vertices of quadrilateral ABCDare A(2,4),B(6,2),C(2, 6), and D(1, 2).a.Show that two sides of the quadrilateral are parallel.b.Show that the quadrilateral has two right angles.21ml1l2If the slopes of two non-vertical lines in the coordinate plane are equal, thenthe lines are parallel.Parallel Lines in the Coordinate Plane343l1kl2xy
SolutionThe slope of .The slope of .The slope of .The slope of .a.and are parallel because they haveequal slopes.b.The slope of is the negative reciprocal ofthe slope of , so they are perpendicular.Therefore,Bis a right angle.The slope of is the negative reciprocal of the slope of , so they areperpendicular. Therefore,Ais a right angle.Answersa.b.Aand Bare right angles.EXAMPLE 2Write an equation for l1, the line through (2, 5) that is parallel to the line l2whose equation is 2xy7.Solution(1) Solve the equation of l2for y:(2)Find the slope of l2. The slope of a line in slope-intercept form is the coefficient of x:(3)Find the slope of l1, which is equal to the slope of l2:(4)Use the definition of slope to write an equation of l1. Let (x, y) and (2, 5) be two points on l1:Answery 2x 1 or 2x y1DABCDAABBCABDABCDA5242222(21)52635 22CD5226212252423543BC562(22)22658245 22AB5222(24)622524512344Parallel LinesOCBAD1yx12xy7y2x7y2x7slope of l12slope2y5 2(x2)y5 –2x4y2x1y25x2(22)y12y2x12x2slope