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Alissa Hancock 2022-07-01 Answered
For f ( t ) = ( 1 2 t - 3 , t t 2 + 1 ) what is the distance between f(0) and f(1)?
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Answers (1)

Elijah Benjamin
Answered 2022-07-02 Author has 10 answers
Step 1
Find the points, then use the distance formula to calculate the distance between them.
f ( t ) = ( x ( t ) , y ( t ) )
The first part the parametric equation gives the x coordinate and the second part gives the y coordinate.
f ( 0 ) = ( 1 2 ( 0 ) - 3 , 0 0 2 + 1 ) = ( - 1 3 , 0 )
f ( 1 ) = ( 1 2 ( 1 ) - 3 , 1 1 2 + 1 ) = ( - 1 , 1 2 )
The distance between ( x 1 , y 1 ) and ( x 2 , y 2 ) is d = ( x 2 - x 1 ) 2 + ( y 2 - y 1 ) 2 so the distance between f ( 0 ) and f ( 1 ) is given by:
d = ( - 1 - ( - 1 3 ) ) 2 + ( 1 2 - 0 ) 2
d = ( - 2 3 ) 2 + ( 1 2 ) 2
d = 4 9 + 1 2 = 17 18 = 17 3 2
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