Question

1. which of the following describes the sequence of transformations shown from figure a to figure a to figure a? a rotate 90 degrees clockwise around the origin and then translate down. b reflect across the x - axis and then reflect across the y - axis. c reflect across the x - axis and then rotate 90 degrees clockwise around the origin. d translate up and then rotate 90 degrees counterclockwise about the origin.

Explanation:

Step1: Analyze rotation

A 90 - degree clockwise rotation around the origin has the transformation rule \((x,y)\to(y, - x)\).

Step2: Analyze reflection across x - axis

Reflection across the x - axis has the rule \((x,y)\to(x, - y)\).

Step3: Check option A

If we first rotate 90 degrees clockwise around the origin and then translate down, it doesn't match the transformation from A to A' and then to A''.

Step4: Check option B

If we reflect across the x - axis and then across the y - axis, the combined transformation \((x,y)\to(-x,-y)\) doesn't match.

Step5: Check option C

First, reflect across the x - axis \((x,y)\to(x, - y)\), then rotate 90 degrees clockwise around the origin \((x, - y)\to(-y,-x)\) which matches the transformation from A to A' to A''.

Step6: Check option D

Translate up and then rotate 90 degrees counter - clockwise \((x,y)\to(-y,x)\) after translation doesn't match.

Answer:

C. Reflect across the x - axis and then rotate 90 degrees clockwise around the origin.