You may also like
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?
Copyright © 1997 - 2021. University of Cambridge.
All rights reserved.
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.