Weekly Problem 14 - 2012
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Here is a set of axes with one shape drawn in the first
What is this shape called? What are the coordinates of the
points A, B, C and D which form the corners of the shape?
Translate (or move) the shape 3 squares to the left and 4
squares up. What are its new coordinates?
Compare these with the original coordinates. Do you notice about
Start with the shape above again. This time reflect it in the x
axis. What are the coordinates of the corners now?
What do you see when you compare these coordinates with the
Predict what the new coordinates would be after a reflection in the
Plot these three points on the graph:
Join the points to make a straight line.
This line is called y = -x because at any point on the line the x
coordinate is the same as its y coordinate, but negative.
Reflect the starting shape in the line y = -x and give the new
coordinates for A, B, C and D.
Look carefully at these new coordinates and then predict what would
happen to these points if they were reflected in the line y =
Now take the original shape again and rotate it 90 o
anticlockwise about the origin. What do you notice about the new
How else could you describe this transformation?