https://file.aiquickdraw.com/mathbot/file/1727294302299gto9uoxm.jpg

To solve this problem, we need to rotate the point \( E(5, 3) \) by 90° counterclockwise around the origin.

The rule for rotating a point \( (x, y) \) by 90° counterclockwise is to transform it into \( (-y, x) \).

Let’s apply this to \( E(5, 3) \):

1. The x-coordinate of \( E \) is 5, and the y-coordinate is 3.
2. After a 90° counterclockwise rotation:
   \[
   E'(x', y') = (-y, x) = (-3, 5)
   \]

So, the new coordinate of \( E' \) is \( (-3, 5) \).

### Final Answer:
The coordinate of \( E' \) is \( (-3, 5) \).

---

Do you need any further details or clarification on this process? Here are some related questions to deepen your understanding:

1. What would the coordinates of \( D'(1, 3) \) be after a 90° counterclockwise rotation?
2. How would you rotate the point \( F(7, -1) \) by 90° counterclockwise?
3. What is the rule for a 90° clockwise rotation?
4. What is the geometric meaning of rotating a shape around the origin?
5. How would you find the coordinates of \( G'(1, -1) \) after a 90° counterclockwise rotation?

**Tip:** When performing a 90° rotation, remember that the x-coordinate and y-coordinate switch places, and one of the signs changes depending on the direction of rotation.

Trapezoid DEFG has vertices D(1, 3), E(5, 3), F(7, -1) and G(1, -1). Imagine the image D'E'F'G' after a 90° counterclockwise rotation about the origin. Enter the coordinate of E'.

Learn how to find the new coordinates of point E after a 90° counterclockwise rotation around the origin. This problem involves geometric transformations and coordinate plane rules. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation