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Weekly Problem 14 - 2012

Weekly Problem 14 - 2012

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Ten Hidden Squares

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

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Cops and Robbers

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

Transformation Tease

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Amy, David, Euan, Lewis and Robert at St. Nicolas School, Newbury tried solving this problem. They have explained their solution very clearly although it is quite long!

The shape ABCD is a trapezium. We think the coordinates are A (4,2) B (6,2) C(7,1) D (3,1)

After moving 3 squares left and 4 up the new coordinates are A (1,6) B (3,6) C (4,5) D (0,5). We noticed that the x coordinate of the new number was 3 less than the original coordinate and the y coordinate was 4 more than the original coordinate.

We reflected the shape in the x axis. The new coordinates are A (4,-2) B(6,-2) C (7,-1) D (3,-1). The x coordinate stayed the same but the y coordinate has got a minus in front of it. We predicted the new coordinates after reflecting in the y axis A (-4,2) B (-6,2) C (-7,1) D (-3,1)

We reflected the original shape in the line y = -x. The new coordinates we found were A (-2,-4) B (-2,-6) C (-1,-7) D (-1,-3). These coordinates are the ones we came up with when we predicted reflecting the 3 points in the line y = -x. (-4,-2) (4,-6) (5,5)

When we took the original shape and rotated it anticlockwise about the origin, we came up with these coordinates A (-2,4) B (-2,6) C (-1,7) D (-1,3)

Looking at the patterns we found, this transformation could also be described as reflecting in the line y = -x and then reflecting in the x axis.
Example A starts (4,2), after reflecting in the line y = -x it is (-2,-4), and then reflecting in the x axis it is (-2,4), which is the same as rotating through 90 degrees.

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