The points are , , and , and the transformation is .
The images , , and under the transformation are as follows:
Now, plot all the points and their images on the coordinate plane as shown below.
From the graph it can be observed that the points A, B, C and their images , , are at same distance from the y-axis.
The points are , , and . The transformation is .
Let and be any two points. The image of the points under the transformation is:
To find the distance between two points, use the following distance formula.
The distance between points P and Q is:
The distance between points and is:
Hence, it is proved that the transformation R is an isometry.
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