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A Tilted Square

Age 14 to 16 Challenge Level:
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The original square had corners (5,5), (5,6), (6,6) and (6,5). Make some different squares.


A corner is “opposite" another corner if they have no line directly between them.

Make a square where the corners (5,3) and (5,7) are opposite each other.


A square is “tilted” if it has no vertical sides. The square you were just asked to draw is an example of a tilted square.

Make another tilted square, this one with corners (5,3) and (6,6) opposite each other.

How do you know that what you have drawn is a square?


Which of these collections of points describes a square?

A) (8,3), (7,8), (2,7), (3,2)
B) (3,3), (7,4), (8,8), (4,7)
C) (16,19), (18,22), (21,20), (19,17)
D) (4,20), (21,19), (20,2), (3,3)

What is special about sets of points that make a square?


Write down all the squares that have corners (61, 26) and (78, 43).
(Note: these do not need to be opposite).


The opposite vertices of a square have coordinates (a,b) and (c,d).

What are the coordinates of the other two vertices?