Symmetry

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SAT Math › Symmetry

Questions 1 - 3
1

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:

2

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

II only

III only

I only

I, II, and III

None of these

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.

or

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.

3

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

III only

II only

I only

I, II and III

None of these

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.

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