# SAT II Math I : Symmetry

## Example Questions

### Example Question #1 : Coordinate Geometry

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:

### 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

None of these

II only

I, II and III

I only

III 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.