Explanation Given information : The line y − 8 = m ( x + 1 ) is at distance 5 units from point ( 2 , 4 ) . Formula used : The distance d of line a line a x + b y + c = 0 from point P ( h , k ) is given by d = | a h + b k + c a 2 + b 2 | Proof: The line y − 8 = m ( x + 1 ) is at distance 5 units from point ( 2 , 4 ) . The equation of given line in standard form is m x − y + ( m + 8 ) = 0 . The distance d of line a line m x − y + ( m + 8 ) = 0 from point P ( 2 , 4 ) is d = | m ⋅ 2 − 4 + m + 8 m 2 + 1 2 | = | 3 m + 4 m 2 + 1 2 | units. But given d = 5 units

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 1.3, Problem 59PS

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Toshow/prove:There is just one line in the family y−8=m(x+1) that is five units from the point (2,4) .

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Chapter 1.3, Problem 58PS

Chapter 1.3, Problem 60PS

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Toshow/prove: There is just one line in the family y − 8 = m ( x + 1 ) that is five units from the point ( 2 , 4 ) .

Solution Summary: The author proves that there is just one line in the family y-8=m(x+1) that is at distance 5 units from the point

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Toshow/prove:There is just one line in the family y−8=m(x+1) that is five units from the point (2,4) .

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Chapter 1 Solutions