SAT II Math II : Symmetry

Study concepts, example questions & explanations for SAT II Math II

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Example Questions

Example Question #7 : 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

Possible Answers:

I, II, and III

II only

I only

III only

None of these

Correct answer:

II only


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.


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.

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