Question

For the graph to the right, describe the composition of transformations that maps KXH to NGP? Thanks.

Answer 1

As we can see in the graph, the triangle KXH has been reflected both on the y-axis and x-axis and then reduce by a scale factor between 0 and 1.

Reflection on both the y-axis and x-axis can be renamed to a single transformation which is a rotation of 180° about the origin. The transformation rule of a rotation about the origin is (x, y) → (-x, -y).

From the original coordinates of the triangle KXH, after rotation of 180° about the origin, the new coordinates are:

Now, if we compare the coordinates of triangle NGP and the new coordinates after the rotation:

We can see that the new coordinates after rotation was multiplied by 1/2 to form the coordinates of the Triangle NGP.

Hence, after a 180° rotation, the triangle KXH is dilated by a scale factor of 1/2. In symbol, this can be written as:

`D_(0.5)\circ r_((180\degree,O))(KXH)`

Note that instead of using 1/2, we use decimal because the instruction is to use integer or decimal.

The answer is Option D and fill in the box with D sub 0.5 as shown above.