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?
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
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?
This problem offers a good opportunity for students to discuss images and find convincing arguments for their solutions.
Reuben Hersh has written that:
"In the classroom, convincing is no problem. Students are too easily convinced. Two special cases will do it."
This problem offers an opportunity to ensure that students are justified in generalising from the particular cases that they have selected.
Before working on this problem, spend time on Cops and Robbers and Coordinate Patterns to develop students' fluency with coordinates.