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The triangle OMN has vertices on the axes with whole number
coordinates.
Points which have whole number coordinates are called lattice
points.
How many lattice points are there on the hypotenuse MN?

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