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Just Opposite

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?

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Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

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Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

A Tilted Square

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
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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?