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
. . .