Creating Rectangles 2

Directions: Using only the whole numbers 1 through 8 (without repeating any number), 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?



What are the properties of a rectangle?
Which lattice points can be used to create the rectangle? Which lattice points can not be used?



There are 4 different sized rectangles. For each of these there are several translations/reflections of it. This list may or may not be exhaustive but it ‘feels’ complete.

The Big Rectangle: area 16, perimeter 12sqrt(2)

The Big Square: area 20, perimeter 8sqrt(5)

The Small Rectangle: area 8, perimeter 10sqrt(2)

The Small Square: area 17, perimeter 4sqrt(17)

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

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