Slopes of Parallel Lines Questions
A detailed tutorial on how to prove that the slopes of two parallel lines are equal. Questions on parallel lines are also included with their detailed solutions.
Prove that two parallel lines have equal slopes
Questions on parallel lines
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slope of segment AB = (6 - 2) / (2 - 0) = 2 slope of segment DC = (8 - b) / (8 - a) for the segments AB and DC to be parallel, their slopes must be equal, hence the equation 2 = (8 - b) / (8 - a) cross multiply to obtain 8 - b = 16 - 2 a slope of segment BC = (8 - 6) / (8 - 2) = 1 / 3 slope of segment AD = (b - 2) / (a - 0) = (b - 2) / a For the segments BC and AD to be parallel, their slopes must be equal 1 / 3 = (b - 2) / a cross multiply to obtain a = 3 b - 6 We now solve the system of the two equations in a and b obtained above and given by 8 - b = 16 - 2 a a = 3 b - 6 Substitute a by 3 b - 6 in the equation 8 - b = 16 - 2 a to obtain 8 - b = 16 - 2 (3 b - 6) Solve the above equation for b to obtain b = 4 then use any of the two equations to find a a = 6 The coordinates of point D are D(6 , 4)
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More References and LinksEquations of Lines in Different Forms,Tutorial on Equation of Line Line Problems Equations of Line Through Two Points And Parallel and Perpendicular. |