IMC 2009 Q8
8. The diagram shows a figure made from six equal, touching squares arranged with a vertical line of symmetry. A straight line is drawn through the bottom corner \(P\) in such a way that the area of the figure is halved. Where will the cut cross the edge \(XY\)?
- A at \(X\)
- B one quarter the way down \(XY\)
- C half way down \(XY\)
- D three-quarters the way down \(XY\)
- E at \(Y\)
Intermediate Mathematical Challenge 2009, Question 8. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A at \(X\)
The small square on top will be in the upper half of the divided figure. Now consider the figure formed by moving this square to become an extra square on the left of the second row, as shown. It may now be seen from the symmetry of the figure that the line \(PX\) splits the new figure in half – with that small square in the upper half. So the line \(PX\) does the same for the original figure.
Solution © UK Mathematics Trust, from the IMC 2009 solutions.