Question

1. each of the six cards shows a shape. a. which pair of cards shows a shape and its image after a rotation? b. which pair of cards shows a shape and its image after a reflection? 2. the five frames show a shapes different positions. describe how the shape moves to get from its position in each frame to the next. 3. the rectangle seen in frame 1 is rotated to a new position, seen in frame 2. select all the ways the rectangle could have been rotated to get from frame 1 to frame 2. a. 40 degrees clockwise b. 40 degrees counterclockwise c. 90 degrees clockwise d. 90 degrees counterclockwise e. 140 degrees clockwise f. 140 degrees counterclockwise

Explanation:

Step1: Analyze rotation in 1a

Check each pair for rotation - invariant shapes.

Step2: Identify rotation pair

Cards 2 and 6 show a shape and its rotated image.

Step3: Analyze reflection in 1b

Look for mirror - like images among pairs.

Step4: Identify reflection pair

Cards 1 and 5 show a shape and its reflected image.

Step5: Analyze movement in 2

Observe position changes between frames.
From Frame 1 to 2: Moves right. From 2 to 3: Moves up and rotates. From 3 to 4: Moves down and rotates back. From 4 to 5: Moves left.

Step6: Analyze rotation in 3

Estimate the angle of rotation from Frame 1 to 2.
The rectangle could be rotated 140 degrees clockwise or 40 degrees counter - clockwise.

Answer:

1a. Cards 2 and 6
1b. Cards 1 and 5

1. From Frame 1 to 2: Moves right. From 2 to 3: Moves up and rotates. From 3 to 4: Moves down and rotates back. From 4 to 5: Moves left.
2. B. 40 degrees counterclockwise, E. 140 degrees clockwise