Explanation Formula used: The equation of a line is of the form y = m x + c , where m is the value of the slope. Perpendicular Theorem: If two lines are perpendicular then the product of their slopes will be negative reciprocal of each other. If m is the slope of line y = m x + c and n is the slope of line perpendicular to y = m x + c then m = − 1 n . Pythagorean Theorem: In a right-angled triangle the square of the hypotenuse is equal to the sum of squares of the other two sides. Proof: Suppose that y = m 1 x + b 1 and y = − m 2 x + b 2 be the equations of two lines. The figure of y = m 1 x + b 1 and y = − m 2 x + b 2 is as follows: From the figure the vertical line is at x = 1 and Δ A B C is a right-angle triangle. Now, apply Pythagorean Theorem on Δ A B C , ( m 1 − m 2 ) 2 = a 2 + b 2 m 1 2 + m 2 2 − 2 m 1 m 2 =

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134437767

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

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Chapter 1.2, Problem 88E

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To prove: The perpendicular property by using point-slope formula and the Pythagorean Theorem assuming that both the lines pass through the origin.

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Chapter 1.2, Problem 87E

Chapter 1.2, Problem 89E

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Finite Mathematics & Its Applications (12th Edition)

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To prove: The perpendicular property by using point-slope formula and the Pythagorean Theorem assuming that both the lines pass through the origin.

Solution Summary: The author proves the perpendicular property by using point-slope formula and Pythagorean Theorem assuming that both the lines pass through the origin.

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To prove: The perpendicular property by using point-slope formula and the Pythagorean Theorem assuming that both the lines pass through the origin.

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Chapter 1 Solutions