Question

1. which of these sequences of transformations would not return a shape to its original position? 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° counterclockwise around center c, then rotate 220° counterclockwise around c again.

Explanation:

Step1: Analyze Option A

Translate \(3\) units up: \(y = y+3\). Then translate \(3\) units down: \(y=(y + 3)-3=y\).

Step2: Analyze Option B

Reflect over line \(p\) once, then reflect over line \(p\) again. A reflection over the same line twice is equivalent to the identity transformation.

Step3: Analyze Option C

Translate \(1\) unit to the right: \(x=x + 1\). Then translate \(4\) units to the left: \(x=(x + 1)-4=x-3\). Then translate \(3\) units to the right: \(x=(x-3)+3=x\).

Step4: Analyze Option D

Rotate \(120^{\circ}\) counter - clockwise: \(\theta=\theta + 120^{\circ}\). Then rotate \(220^{\circ}\) counter - clockwise: \(\theta=(\theta + 120^{\circ})+220^{\circ}=\theta+340^{\circ}
eq\theta\) (mod \(360^{\circ}\)).

Answer:

D. Rotate \(120^{\circ}\) counterclockwise around center \(C\), then rotate \(220^{\circ}\) counterclockwise around \(C\) again.