What is the image of the point left parenthesis, minus, 3, comma, 5, right parenthesis(−3,5) after a rotation of 90, degrees90 
∘
  counterclockwise about the origin?

To find the image of a point after a \(90^\circ\) counterclockwise rotation about the origin, we can use the following rule:

- The image of \((x, y)\) after a \(90^\circ\) counterclockwise rotation becomes \((-y, x)\).

Given the point \((-3, 5)\), we apply this transformation:

\[
(x, y) = (-3, 5) \quad \rightarrow \quad (-y, x) = (-5, -3)
\]

So, the image of the point \((-3, 5)\) after a \(90^\circ\) counterclockwise rotation about the origin is \((-5, -3)\).

Would you like more details or have any questions? Here are some related questions:

1. What is the formula for rotating a point \(180^\circ\) about the origin?
2. How would you rotate a point \(270^\circ\) counterclockwise about the origin?
3. What is the image of the point \((4, -2)\) after a \(90^\circ\) counterclockwise rotation?
4. How do you reflect a point across the x-axis and y-axis?
5. How would you describe a \(90^\circ\) clockwise rotation about the origin?

**Tip:** To remember rotations, it's helpful to visualize the coordinate plane and imagine moving counterclockwise or clockwise around the origin.

What is the image of the point (-3, 5) after a rotation of 90 degrees counterclockwise about the origin?

Discover how to find the image of the point (-3, 5) after a 90-degree counterclockwise rotation about the origin. This problem covers key geometric concepts and the rotation formula, making it suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation