Question

Which transformation gives the same result as a rotation of 180° around the origin followed by a reflection over the x-axis?

Answer 1

This transformation is equivalent to 'Rotating 180 degree around the origin'.

Explanation:

To find : Which transformation gives the same result as a rotation of 180° around the origin followed by a reflection over the x-axis?

Solution :

We know that, reflection means to flip the figure over a line.

Now, as first the figure is reflected over the y- axis, the change in any tuple (x,y) becomes (-x,y).

Furthermore, the figure is reflected over the x-axis, then the change in tuple (-x,y) becomes (-x,-y).

Finally, after reflection over y-axis followed by reflection over x-axis gives that (x,y) changes to (-x,-y).

This is the same result obtained after rotating the figure or points 180 degree around the origin (0,0).