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Math Help - Co-ordinate Geometry: Colinear points

  1. #1
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    Question Co-ordinate Geometry: Colinear points

    A, B and C are three colinear points. A and B are respectively (3,4) and (7,7) and AC is equal to 10 units. Find the coordinates of C.
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  2. #2
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    Quote Originally Posted by Ilsa View Post
    A, B and C are three colinear points. A and B are respectively (3,4) and (7,7) and AC is equal to 10 units. Find the coordinates of C.
    Let h,k)" alt="Ch,k)" />. From the given we know:
    \displaystyle\frac{7-4}{7-3}=\displaystyle\frac{7-k}{7-h} and (h-3)^2+(k-4)^2=100.

    Solve for h~\&~k.
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  3. #3
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    could u pls explain which formula u have used?
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  4. #4
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    Quote Originally Posted by Ilsa View Post
    could u pls explain which formula u have used?
    Slope: collinear points determine the same slope.
    Distance.
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  5. #5
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    Hello, Ilsa!

    Did you make a sketch?


    A, B, C are three collinear points.
    A and B are (3,4) and (7,7), respectively,
    and AC is equal to 10 units.
    Find the coordinates of C.
    Code:
          |                                      C
          |                                      o
          |                                  *   :
          |                              *       :3
          |                      B   *           :
          |                 (7,7)o - - - - - - - +
          |                  *   :       4
          |              *       :3 
          |      A   *           :
          | (3,4)o - - - - - - - +
          |             4
          |
          |
        - + - - - - - - - - - - - - - - - - - - - - -
          |

    To go from point A to point B, we move: right 4, up 3.

    The length of AB is: . \sqrt{4^2+3^2} \:=\:\sqrt{25} \:=\:5


    Since the length of AC is 10, then: . BC = 5.

    To go from point B to point C, we move (again): right 4, up 3.


    Therefore, point C is at: . (11,10)
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  6. #6
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    pls sir i wud be grateful of u if u pls help me doing the sum in intermediate level or ordinary level or according to the ratio theorem or distance formula
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