Reflections

Weekly Problem 28 - 2013
Two lines meet at a point. Another line through this point is reflected in both of these lines. What is the angle between the image lines?

Weekly Problem 35 - 2012
How many more triangles need to be shaded to make the pattern have a line of symmetry?

What is the missing symbol? Can you decode this in a similar way?

Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

What happens to these capital letters when they are rotated through one half turn, or flipped sideways and from top to bottom?

How many different symmetrical shapes can you make by shading triangles or squares?

In how many ways can you fit all three pieces together to make shapes with line symmetry?

Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.