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SAT II Math II : Symmetry

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Example Question #1 : Symmetry

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

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

I) Symmetry with respect to the origin

II) Symmetry with respect to the $\displaystyle x$ -axis

III) Symmetry with respect to the $\displaystyle y$ -axis

Possible Answers:

None of these

I, II, and III

III only

II only

I only

Correct answer:

II only

Explanation:

The relation

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

is a circle with center (h,k) $\displaystyle (h,k)$ and radius $\displaystyle r$ .

In other words, it is a circle with center at the origin, translated right $\displaystyle h$ units and up $\displaystyle k$ units.

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

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

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

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SAT II Math II : Symmetry

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

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Example Question #1 : Symmetry

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