For f ( t ) = ( 1 2 t - 3 , t t 2 + 1 ) what is the distance between f(0) and f(1)?

Question

For             f              (        t        )              =          (              1                  2          t          -          3                    ,              t                                            t              2                        +            1                              )       what is the distance between f(0) and f(1)?

Elijah Benjamin · Accepted Answer

Step 1Find 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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