Explanation The equation of the line segment joining P ( − 2 , 3 ) and Q ( 2 , − 3 ) can be given by using two-point form as shown below. y − 3 − 3 − 3 = x + 2 2 + 2 y − 3 − 6 = x + 2 4 4 y − 12 = − 6 x − 12 3 x + 2 y = 0 Therefore, the slope of the line is − b a = − 3 2 . Hence, b = − 3 2 a . Let a = 2 then, b = − 3 . Parametric equation of the line through the point ( x 0 , y 0 ) is x = x 0 + a t , y = y 0 + b t . Let, P ( − 2 , 3 ) = ( x 0 , y 0 ) then, x = x 0 + a t = − 2 + 2 t y = y 0 + b t = 3 − 3 t Thus, the parametric equation is x = − 2 + 2 t , y = 3 − 3 t ; 0 ≤ t ≤ 2 . At t = 0 the point is ( − 2 + 2 t , 3 − 3 t ) = ( − 2 , 3 ) and at t = 2 the point is ( − 2 + 2 t , 3 − 3 t ) = ( 2 , − 3 ) . Thus, the parametric equation of the line segment joining P ( − 2 , 3 ) and Q ( 2 , − 3 ) is x = − 2 + 2 t , y = 3 − 3 t ; 0 ≤ t ≤ 2 . Similarly, the equation of the line segment joining Q ( 2 , − 3 ) and R ( 3 , 5 ) can be given by using two-point form as shown below. y − 5 − 3 − 5 = x − 3 2 − 3 y − 5 − 8 = x − 3 − 1 y − 5 = − 8 x + 24 y = 8 x + 29 Therefore, the slope of the line is 8

Calculus: Single Variable, Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)

3rd Edition

ISBN: 9780134996714

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Chapter 12.1, Problem 47E

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To find: The parametric equation for the linear path joining P(−2,3) to Q(2,−3) to R(3,5) for 0≤t≤2 and sketch the curve showing the positive orientation.

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Chapter 12.1, Problem 46E

Chapter 12.1, Problem 48E

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Calculus: Single Variable, Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)

Ch. 12.1 - Identify the graph generated by the parametric...Ch. 12.1 - Prob. 2QC Ch. 12.1 - Prob. 3QC Ch. 12.1 - Prob. 4QC Ch. 12.1 - Prob. 5QC Ch. 12.1 - Prob. 6QC Ch. 12.1 - Explain how a pair of parametric equations...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E

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The parametric equation for the linear path joining P ( − 2 , 3 ) to Q ( 2 , − 3 ) to R ( 3 , 5 ) for 0 ≤ t ≤ 2 and sketch the curve showing the positive orientation.

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To find: The parametric equation for the linear path joining P(−2,3) to Q(2,−3) to R(3,5) for 0≤t≤2 and sketch the curve showing the positive orientation.

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Chapter 12 Solutions