Question 295864: How many different (noncongruent) convex quadrilateral can you make on a 3-by-3 dot grid, using the dots as vertices?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Number your dots, left to right, then top to bottom.
You can make a square with 1,2,4,5. But that is congruent to any other square with side measuring 1.
You can make a larger square with 1,3,7,9. There is obviously only one of those that can be made.
You can make a rectangle with 1, 3, 4, 6.
You can make a parallelogram with 2,3,4,5. All other parallelograms of this size are congruent.
You can make a larger parallelogram with 2, 3, 7, and 8
You can make a trapezoid with 2, 3, 4, 6
You can make a larger trapezoid with 3, 4, 7, 9
So, two squares, a rectangle, two parallelograms, and two trapezoids (or trapeziums if you are British) for a total of 7.
John
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