Question

i can identify the sequence when a rotation, reflection, and/or translation is applied. 1. here are three pairs of figures. a. which transformation takes figure a to figure b in pair 1: a translation, rotation, or reflection? b. which transformation takes figure a to figure b in pair 2: a translation, rotation, or reflection? c. which transformation takes figure a to figure b in pair 3: a translation, rotation, or reflection? 2. all of these sequences of transformations would return a shape to its original position except? a. translate 3 units up, then 3 units down. b. reflect over line p, then reflect over line p again. c. translate 1 unit to the right, then 4 units to the left, then 3 units to the right. d. rotate 120° counter - clockwise around center c, then rotate 220° counter - clockwise around c again. explain your reasoning.

Explanation:

Step1: Analyze translations

Translation moves a shape without rotating or flipping it. Repeated translations in opposite - directions can cancel each other out.

Step2: Analyze rotations

Rotations around a point. A full - rotation is 360°. If the sum of rotation angles is a multiple of 360°, the shape returns to its original orientation.

Step3: Analyze reflections

Reflections over the same line twice return a shape to its original position.

For Part 1:

• Visually, we can see that to get from Figure A to Figure B, we can first translate Figure A to the right (a translation). Then we rotate it (a rotation). There is no reflection.

For Part 2:

• To get from Figure A to Figure B, we can translate Figure A down and to the left (a translation), then rotate it (a rotation). There is no reflection.

For Part 3:

• To get from Figure A to Figure B, we can translate Figure A to the left (a translation), then rotate it (a rotation). There is no reflection.

For the second question about the sequence of transformations that would return a shape to its original position:

• Option A: Translating 3 units up and 3 units down is a translation that cancels out. But there is no other operation to reverse any non - translation operations if present.
• Option B: Reflecting over line p twice returns the shape to its original position with respect to the reflection operation.
• Option C: Translating 1 unit to the right, 4 units to the left, and 3 units to the right: \(1 - 4+3 = 0\), the net translation is 0. But there is no information about reversing rotations or other non - translation operations.
• Option D: \(120^{\circ}+220^{\circ}=340^{\circ}

eq360^{\circ}\), and just rotating around a point twice with these angles does not return the shape to its original position in most cases.

Answer:

Part 1: Translation, Rotation
Part 2: Translation, Rotation
Part 3: Translation, Rotation

1. B. Reflect over line p, then reflect over line p again.