QQuestionMathematics
QuestionMathematics
Write a rule for rotating 270 degrees clockwise about the origin.
A. (x,y)→(−y,x)
B. (x,y)→(y,−x)
C. (x,y)→(−x,−y)
D. (x,y)→(x,−y)
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 Rotation Conventions
- Positive rotation is typically counterclockwise - A 270 -degree clockwise rotation is equivalent to a 90 -degree counterclockwise rotation
Step 3:: Visualize the Rotation
- Start with point (x,y) - Rotate 90 degrees counterclockwise - This means the point will move from its original position to a new position
Step 4:: Determine the Coordinate Transformation
- When rotating 90 degrees counterclockwise: * x-coordinate becomes -y * y-coordinate becomes x
Step 5:: Write the Transformation Rule
\begin{pmatrix} x \ y \end{pmatrix} \rightarrow \begin{pmatrix} -y \ x \end{pmatrix}
Step 6:: Check the Given Options
- This matches option A: (x,y) → (−y,x)
Final Answer
Verification: - If you start at (1,2) and rotate 270 degrees clockwise - You'll end up at (- 2,1), which follows the rule (x,y) → (−y,x)
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