Question

a sequence of rigid motions creates the following pattern.
match each statement with the sequence of rigid motions that shows the patterns are congruent.
a sequence may be used more than once.
statement
the pattern in quadrant i
is congruent to the pattern
in quadrant ii.
the pattern in quadrant ii
is congruent to the pattern
in quadrant iii.
the pattern in quadrant iii
is congruent to the pattern
in quadrant iv.
the pattern in quadrant iv
is congruent to the pattern
in quadrant i.
the pattern in quadrant i
is congruent to the pattern
in quadrant iii.
sequence of rigid motions
a 180° rotation around
the origin
a 90° counterclockwise rotation
around the origin
a reflection across the
y - axis followed by a
90° counterclockwise
rotation around the origin
a 90° counterclockwise rotation
around the origin followed
by a reflection across the y - axis
a reflection across the x - axis

Explanation:

Step1: Analyze the first statement

The pattern in Quadrant I is congruent to the pattern in Quadrant II. A reflection across the \(y\) - axis followed by a \(90^{\circ}\) counterclockwise rotation around the origin will map the pattern from Quadrant I to Quadrant II.

Step2: Analyze the second statement

The pattern in Quadrant II is congruent to the pattern in Quadrant III. A \(90^{\circ}\) counterclockwise rotation around the origin will map the pattern from Quadrant II to Quadrant III.

Step3: Analyze the third statement

The pattern in Quadrant III is congruent to the pattern in Quadrant IV. A reflection across the \(x\) - axis will map the pattern from Quadrant III to Quadrant IV.

Step4: Analyze the fourth statement

The pattern in Quadrant IV is congruent to the pattern in Quadrant I. A \(90^{\circ}\) counterclockwise rotation around the origin followed by a reflection across the \(y\) - axis will map the pattern from Quadrant IV to Quadrant I.

Step5: Analyze the fifth statement

The pattern in Quadrant I is congruent to the pattern in Quadrant III. A \(180^{\circ}\) rotation around the origin will map the pattern from Quadrant I to Quadrant III.

Answer:

1. A reflection across the \(y\) - axis followed by a \(90^{\circ}\) counterclockwise rotation around the origin
2. A \(90^{\circ}\) counterclockwise rotation around the origin
3. A reflection across the \(x\) - axis
4. A \(90^{\circ}\) counterclockwise rotation around the origin followed by a reflection across the \(y\) - axis
5. A \(180^{\circ}\) rotation around the origin