https://file.aiquickdraw.com/mathbot/file/1726135697628ijl9cs3i.jpg

To determine the new coordinates of the vertices after a 90-degree clockwise rotation around the origin, we use the rotation transformation rule for 90 degrees clockwise, which swaps the x and y coordinates and changes the sign of the new y-coordinate. The formula to rotate a point \((x, y)\) 90 degrees clockwise around the origin is:

\[
(x', y') = (y, -x)
\]

Based on the image:

- The original coordinates of \(T\) are \((-5, -1)\).
- The original coordinates of \(U\) are \((-2, -1)\).
- The original coordinates of \(V\) are \((-2, -4)\).
- The original coordinates of \(W\) are \((-5, -4)\).

Applying the rotation formula:

- \(T'\) after 90 degrees clockwise rotation: \((y, -x) = (-1, 5)\)
- \(U'\) after 90 degrees clockwise rotation: \((y, -x) = (-1, 2)\)
- \(V'\) after 90 degrees clockwise rotation: \((y, -x) = (-4, 2)\)
- \(W'\) after 90 degrees clockwise rotation: \((y, -x) = (-4, 5)\)

These coordinates are based on the visible grid in the photo and the transformation rules for a 90-degree clockwise rotation.

If you have any further questions or need additional details, feel free to ask! Here are some related questions you might consider:

1. What would the coordinates be after a 180-degree rotation?
2. How would the coordinates change if the rotation were counterclockwise instead?
3. What is the significance of the origin in rotation transformations?
4. How does changing the point of rotation affect the outcome of the transformation?
5. Can you explain how to determine the rotation matrix for different degrees of rotation?

**Tip**: To check the accuracy of your rotated coordinates, try plotting the original and transformed points on graph paper or using a digital graphing tool to visualize the transformations.

Write the coordinates of the vertices after a rotation 90° clockwise around the origin.

Learn how to calculate the coordinates of a shape's vertices after a 90° clockwise rotation around the origin. This example includes key concepts from coordinate geometry and transformation rules, suitable for Grades 7-9 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation