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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?
Hypotenuse Lattice Points
The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?
Beelines
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Age 14 to 16 Challenge Level:
A cube (1 metre by 1 metre by 1 metre) has one face on the ground and one face pushed up against a wall.
A 4 metre long ladder is leaning against the wall, just touching the cube.
A 4 metre long ladder is leaning against the wall, just touching the cube.
How high is the top of the ladder above the ground?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.