Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 7 Geometry
Problem
1) A circle is enlarged by increasing its radius by 50%. What is the ratio of the area of the enlarged circle to the area of the original circle? You may express your answer as a fraction. (Hint: you can work with any size radius.)
2) In the diagram there are two parallel line segments and a labeled line segment R that meets the line segments at a 30 degree angle. Sketch what the result is when you reflect the two parallel line segments across R. What are the measures of the new angles formed between the reflected line segments and line segment R?
3) Which of the following nets will correctly fold to make a triangular prism with one pointed tetrahedron side?
(Think of a pointed three sided stake.)

Problem
4) In triangle ABC shown, AB is perpendicular to CB, and DE is parallel to AC. The angle at vertex A measures 42 degrees. What is the measure of angle DEC with the label y?
5) When you translate triangle ABC 5 units east, 4 units north, 7 units west and finally 9 units south, what are the final coordinates for vertex B?