

Recall that, for a general point ๐ ( ๐ฅ, ๐ฆ ), a reflection in the ๐ฅ - a x i s maps

The coordinates of the corresponding image points. We can then use the above transformation to work out Here, our first step is to read off the coordinates of the vertices of the quadrilateral. This means it maps point ๐ onto the image point ๐ โฒ by changing the sign of the ๐ฅ-coordinate Recall that, for a general point ๐ ( ๐ฅ, ๐ฆ ), a reflection in the ๐ฆ - a x i s maps Next, we shall examine reflection in the ๐ฆ - a x i s, which follows a very similar pattern to reflection in the ๐ฅ - a x i s. We conclude that the pair of triangles ๐ด and ๐ต represent a reflection in the ๐ฅ - a x i s. Triangle ๐ต, we would have found that the image points were the vertices of triangle ๐ด. Moreover, if we had started with the vertices of It is easy to check that these image points are precisely the vertices shown for triangle ๐ต. Using the fact that ๐ ( ๐ฅ, ๐ฆ ) โ ๐ โฒ ( ๐ฅ, โ ๐ฆ ), we find the image points as follows: Reading off from the diagram, we see that triangle ๐ด has vertices with coordinates ( โ 3, 5 ), ( โ 2, 2 ), and ( โ 5, 3 ). Although this should be obvious from the diagram, we will use the definition of a reflection in

However, as there is no such triangle, then ๐ถ has not been reflected in the ๐ฅ - a x i s, so the reflected triangles must be
