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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?

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Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

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Isosceles Triangles

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Route to Infinity

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Take a look at the co-ordinates of the points along the route.

What do you notice about the order in which the route visits the points?

When do the arrows point up, and when do they point down?