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Thread: 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 $\displaystyle Ch,k)$. From the given we know:
    $\displaystyle \displaystyle\frac{7-4}{7-3}=\displaystyle\frac{7-k}{7-h}$ and $\displaystyle (h-3)^2+(k-4)^2=100$.

    Solve for $\displaystyle h~\&~k$.
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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?


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

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

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


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

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


    Therefore, point C is at: .$\displaystyle (11,10)$
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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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