For f ( t ) = ( t e 1 - 3 t , 2 t 2 - t ) what is the distance between f(2) and f(5)?

Question

For             f              (        t        )              =          (      t              e                  1          -          3          t                    ,      2              t        2            -      t      )       what is the distance between f(2) and f(5)?

Smarmabagd7 · Accepted Answer

Step 1We have:             f              (        t        )              =          (      t              e                  1          -          3          t                    ,      2              t        2            -      t      )      When       t    =    2   we have:            f              (        2        )              =          (      2              e                  1          -          6                    ,      2      ⋅      4      -      2      )                                               =          (      2              e                  -          5                    ,      6      )      When       t    =    5   we have:            f              (        5        )              =          (      5              e                  1          -          15                    ,      2      ⋅      25      -      5      )                                               =          (      5              e                  -          14                    ,      -      45      )      Step 2So, using Pythagoras, the distance, d, between these coordinates is given by:            d      2        =                  (        2                  e                      -            5                          -        5                  e                      -            14                          )            2        +                  (        6        -                  (          -          45          )                )            2                           =                  (        2                  e                      -            5                          -        5                  e                      -            14                          )            2        +                  (        6        +        45        )            2                           =                  (        2                  e                      -            5                          -        5                  e                      -            14                          )            2        +          51      2      Therefore,       d    =                                        (            2                          e                              -                5                                      -            5                          e                              -                14                                      )                    2                +                  51          2                                    ≈    51         u    n    i    t    s

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