# SAT II Math I : Symmetry

## Example Questions

### Example Question #1 : Symmetry

Given a point , what is the new value if this point is flipped across the line ?      Explanation:

The displacement between negative three and positive one is four. This mean that after flipping the point, it must be symmetrical to its original location.   The new point must also be 4 units to the right of the line.

The new point would be located at: The answer is: ### Example Question #2 : Symmetry

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

I, II and III

II only

None of these

III only

I only

III 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 (the radius is irrelevant to the question). or is this circle translated right zero units and up 2 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. 