Thread: Coordinate Geometry

Find coordinates for the vertices of a

lattice rectangle that is three times as long as it is wide, with none of the sides horizontal.

Originally Posted by thamathkid1729

Find coordinates for the vertices of a

lattice rectangle that is three times as long as it is wide, with none of the sides horizontal.

A(0, 0)
B(12, 9)
C(15, 5)
D(3, -4)

... but why?

Hello, thamathkid1729!

earboth found an elegant solution!

Find coordinates for the vertices of a lattice rectangle
that is three times as long as it is wide, with none of the sides horizontal.

Select any two points:
. . (In this example:

Code:

      |
      |     P
      |     o(x1,y1)
      |     :\
      |     : \
      |  ∆y :  \
      |     :   \
      |     :    \
      |     + - - o(x2,y2)
      |       ∆x  Q
      |
  - - + - - - - - - - - -
      |

Code:

                                      S
                                    o
                                 *   \
                             *        \
                          *            \  
                       *                \
                    *                    \
                 *                       o R
              *                       *  :
       P   *                       *     :∆x
        o                       * - - - -+
        :\                   *  :   ∆y
        : \               *     :∆x
     ∆y :  \           *- - - - +
        :   \       *  :    ∆y
        :    \   *     :∆x
        + - - o - - - -+
          ∆x  Q    ∆y

. . .

Originally Posted by earboth

A(0, 0)
B(12, 9)
C(15, 5)
D(3, -4)

... but why?

It was a challenge for me...