SAT II Math II : Symmetry

Example Questions

Example Question #2 : Coordinate Geometry

Which of the following symmetries applies to the graph of the relation

?

I) Symmetry with respect to the origin

II) Symmetry with respect to the -axis

III) Symmetry with respect to the -axis

II only

I only

I, II, and III

None of these

III only

II only

Explanation:

The relation

is a circle with center  and radius  .

In other words, it is a circle with center at the origin, translated right  units and up  units.

or

is a circle translated right 4 units and up zero units. The upshot is that the circle moves along the -axis only, and therefore is symmetric with respect to the -axis, but not the -axis. Also, as a consequence, it is not symmetric with respect to the origin.