QQuestionMathematics
QuestionMathematics
Which of the following would be a rule for rotating 90 degrees clockwise?
A. (x, y) → (-x, y)
B. (x, y) → (y, -x)
C. (x, y) → (-x, -y)
D. (x, y) → (-y, x)
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:Let's solve this step by step:
Step 2:: Understand the Rotation Transformation
A 90 -degree clockwise rotation means we need to transform the coordinates (x, y) to a new position that represents a quarter turn clockwise around the origin.
Step 3:: Analyze Each Option
Let's visualize what happens to a point (x, y) when rotated 90 degrees clockwise: - The x-coordinate will change - The y-coordinate will change - The point will move to a new quadrant
Step 4:: Test Each Option
D. $$(x, y) \rightarrow (-y, x)
This is a reflection across the y-axis, not a rotation. This is a 90 -degree counterclockwise rotation, not clockwise. This is a 180 -degree rotation, not 90 degrees. This represents a 90 -degree clockwise rotation.
Step 5:: Verify Option D
- Rotated point: $$(-3, 2)
Let's confirm with an example point (2, 3): This confirms a 90 -degree clockwise rotation.
Final Answer
D. (x, y) \rightarrow (-y, x) is the correct rule for rotating 90 degrees clockwise.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students