More Transformations on a Pegboard
You might like to try
Transformations on a Pegboard before looking at this problem.
Here are some ideas to take this activity some stages further. One
part of the problem was about Billy with a triangle and the other
was about Tanya with her enlarging rectangle.
You may like to use this interactive pegboard to try out your
ideas. Read underneath the interactivity for the challenges!
Full Screen Version
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Billy asked, 'By moving just one peg can you make a right-angled
triangle?'. Well, I had a go starting the same way:
Here are two I found moving one peg each time (from the
original):
And so on and so on . . . . . How many different ones can you get
if you stick to a grid of $7$ rows of dots and $9$ columns of dots?
The triangle started off having a base of $6$ and was $3$ high.
Look at the other triangles you have found that have this same base
and height.
What can you say about the areas of this set of triangles? (You
might like to draw some more triangles with a base of $6$ and a
height of $3$ which don't have right angles to test your
ideas.)