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Math Help - Triangle

  1. #1
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    Triangle

    Given points (0, 14), (18, 4). Find a third point so that the three points form the vertices of an isosceles triangle
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  2. #2
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    Quote Originally Posted by ailmasum View Post
    Given points (0, 14), (18, 4). Find a third point so that the three points form the vertices of an isosceles triangle
    Easiest way is to reflect across y-axis.
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  3. #3
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    Hello, ailmasum!

    Who assigned this problem?
    It's truly silly . . .


    \text{Given points }A(0, -14),\;B(18, 4).

    \text{Find a third point }C\text{ so that }\Delta ABC\text{ is an isosceles triangle.}
    Code:
            |
            |      ♥                B
            |       ♥               o
            |        ♥           *
            |         ♥       *
        - - + - - - - -♥- -*- - - -
            |           *
            |        *   ♥
            |     *       ♥
            |  *           ♥
            o               ♥
            |

    \,C can be (almost) any point on the perpendicular bisector of AB.




    Code:
                  * * *
              *           *   B
            *               o
           *              *  *
                        * 
          *         A *       *
          *         o         *
          *      (0,-14)      *
    
           *                 *
            *               *
              *           *
                  * * *

    Consider the circle with center \,A and radius AB.

    \,C can be (almost) any point on the circle.




    Code:
                  * * *
              *           *
            *               *
           *                 *
    
          *         B         *
          *         o(18,4)   *
          *       *           *
                *
           *  *              *
            o               *
          A   *           *
                  * * *

    Consider the circle with center \,B and radius AB.

    \,C can be (almost) any point on the circle.

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  4. #4
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    Quote Originally Posted by Soroban View Post

    It's truly silly . . .

    I think it's a reasonable enough question. Suppose you were asked to solve it in under 10 seconds, or as part of some rapid-fire competition..
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