Symmetry

SAT Subject Test in Math II · Learn by Concept

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SAT Subject Test in Math II › Symmetry

1 - 1

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

$\left (x- 4 \right )^{2} + y ^{2}= 18$ ?

I) Symmetry with respect to the origin

II) Symmetry with respect to the -axis

III) Symmetry with respect to the -axis

II only

CORRECT

III only

I only

I, II, and III

None of these

Explanation

The relation

$(x-h)^{2} + (y - k)^{2} = r^{2}$

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.

$\left (x- 4 \right )^{2} + y ^{2}= 18$

$\left (x- 4 \right )^{2} +\left ( y - 0 \right ) ^{2}= 18$

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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