For f ( t ) = ( 1 1 - t , - 1 1...

Amber Quinn

Amber Quinn

Answered

2022-06-25

For f ( t ) = ( 1 1 - t , - 1 1 + t 2 ) what is the distance between f(2) and f(5)?

Answer & Explanation

SuefsSeeltHeRn8

SuefsSeeltHeRn8

Expert

2022-06-26Added 8 answers

Step 1
Find the points first:
f ( 2 ) = ( 1 1 - 2 , - 1 1 + 2 2 ) = ( - 1 , - 1 5 )
f ( 5 ) = ( 1 1 - 5 , - 1 1 + 5 2 ) = ( - 1 4 , - 1 26 )
The distance between the points ( x 1 , y 1 ) and ( x 2 , y 2 ) is calculated through d = ( y 2 - y 1 ) 2 + ( x 2 - x 1 ) 2
d = ( - 1 26 - ( - 1 5 ) ) 2 + ( - 1 4 - ( - 1 ) ) 2
d = ( 21 130 ) 2 + ( 3 4 ) 2
Step 2
You can go ahead and make this a decimal answer, but you can also do some nice simplification if you feel up to it.
d = ( 3 7 2 5 13 ) 2 + ( 3 2 2 ) 2
d = 3 2 7 2 2 2 5 2 13 2 + 3 2 2 4
d = 2 2 3 2 7 2 2 4 5 2 13 2 + 3 2 5 2 13 2 2 4 5 2 13 2
d = 3 2 ( 2 2 7 2 + 5 2 13 2 ) 2 4 5 2 13 2
d = 3 2 2 5 13 ( 2 7 ) 2 + ( 5 13 ) 2
d = 3 4421 260 0.767199

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