Directions: Using the digits 1 to 8 at most one time each, fill in the coordinates to create the vertices of a rectangle: A(__, __), B(__, __), C(__, __), D(__, __).
Extension: What is the rectangle with the largest/smallest area/perimeter that you can find?
Hint
Hint
Which lattice points can be used to create the rectangle? Which lattice points can not be used?
Answer
Answer
The Big Rectangle: area 16, perimeter 12sqrt(2)
(1,4)(3,2)(7,6)(5,8)
(1,6)(3,8)(7,4)(5,2)
The Big Square: area 20, perimeter 8sqrt(5)
(1,6)(5,8)(7,4)(3,2)
(1,4)(3,8)(7,6)(5,2)
The Small Rectangle: area 8, perimeter 10sqrt(2)
(1,4)(5,8)(6,7)(2,3)
(1,7)(2,8)(6,4)(5,3)
The Small Square: area 17, perimeter 4sqrt(17)
(1,4)(2,8)(6,7)(5,3)
(2,3)(6,4)(5,8)(1,7)
For each of the rectangles above, an additional rectangle can be created by swapping the x and y coordinates (the reflection about line y=x)
Source: Erick Lee
