So we obtain the image ? ′ from ? by keeping the ?-coordinate the same and changingįor the first part of the question, we must apply the above transformation to the points ? ( 1, 3 ), ? ( 1, 2 ),Īnd ? ( 4, 1 ) this will give us the coordinates of the image points. Recall that, for a general point ? ( ?, ? ), a reflection in the ? - a x i s maps
Here, our first step is to read off the coordinates of the vertices of the quadrilateral. This means it maps point ? onto the image point ? ′ by changing the sign of the ?-coordinate Recall that, for a general point ? ( ?, ? ), a reflection in the ? - a x i s maps Next, we shall examine reflection in the ? - a x i s, which follows a very similar pattern to reflection in the ? - a x i s. We conclude that the pair of triangles ? and ? represent a reflection in the ? - a x i s. Triangle ?, we would have found that the image points were the vertices of triangle ?.
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 ?.
Using the fact that ? ( ?, ? ) → ? ′ ( ?, − ? ), we find the image points as follows: Reading off from the diagram, we see that triangle ? has vertices with coordinates ( − 3, 5 ), ( − 2, 2 ), and ( − 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 ? has not been reflected in the ? - a x i s, so the reflected triangles must be