Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Section 1.2 - The Rectangular Coordinate System - 1.2 Problem Set - Page 24: 40

Answer

y= 0 or 2 Both the values satisfy distance condition.

Work Step by Step

To find y, we will calculate distance between given points, i. e. (7, y) and (3, 3), using distance formula and equate it to the given distance i.e. 5. Thus- $ \sqrt { (x_{2} - x_{1}) ^{2} + (y_{2} - y_{1}) ^{2}}$ = 5 $ \sqrt { (3 - 7) ^{2} + (3- y) ^{2}}$ = 5 $ \sqrt { (-4) ^{2} + (9 -2y + y^{2}) }$ = 5 Squaring on both sides, we get- $ { 16 + (9 -2y + y^{2})}$ = $25$ $ y^{2}-2y + 25$ = $25$ OR $ y^{2}-2y$ = 0 ( adding -25 on both sides) $y (y- 2)$ = 0 (On factorizing) Equating each factor to zero, we get- $y$= 0 or 2 Therefore y may be 0 or 2
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