Question

Select all the sequences of reflections that produce an image equivalent to the image r(180°, O)(△BCD).

Answer 1

Answer:

r(180°,0) is a rotation of 180° degrees over the origin.

Notice that this rotation moves our figure to the opposite quadrant (so a translation of two quadrants).

Then this is equivalent to:

A reflection over the x-axis followed by a reflection over the y-axis.

Or.

A reflection over the y-axis followed by a reflection over the x-axis.

There is another possible reflection, but it depends on where is our figure.

If the figure is in the first or third quadrant, a reflection over the line y = -x is equivalent to the rotation.

If the figure is in the second or third quadrant, then the reflection over the line y = x is equivalent to the rotation.

We can combine those two and write:

A reflection over the line y = (-1)^n*x.

Where n is the number associated with the quadrant where the figure is in.