r(90°, O) (△MN) for M(3, −5), N(2, 4)

To rotate a figure \( \triangle MN \) around the origin \( O \) by \( 90^\circ \), we apply the following transformation rules for a \( 90^\circ \) counterclockwise rotation about the origin:

\[
(x, y) \rightarrow (-y, x)
\]

Given:
- \( M(3, -5) \)
- \( N(2, 4) \)

Applying the transformation to each point:

1. For \( M(3, -5) \):
   \[
   M' = (-(-5), 3) = (5, 3)
   \]

2. For \( N(2, 4) \):
   \[
   N' = (-4, 2)
   \]

### Final Coordinates After Rotation
- \( M' = (5, 3) \)
- \( N' = (-4, 2) \)

Thus, the rotated image \( \triangle M'N' \) has vertices:
- \( M'(5, 3) \)
- \( N'(-4, 2) \)

Would you like more details or have any questions?

---

**Related Questions:**
1. How does rotation work in three-dimensional space?
2. What are other common rotation angles and their transformation rules?
3. How do you find the center of rotation if it’s not the origin?
4. How does a 90° clockwise rotation differ in transformation rules?
5. What happens if the points are rotated by 180°?

**Tip:** When rotating points, always keep track of the direction (clockwise or counterclockwise), as it affects the transformation rules.

Rotate △MN by 90° counterclockwise about the origin O for M(3, −5) and N(2, 4).

This guide covers the step-by-step solution to rotating △MN by 90° counterclockwise about the origin, with vertices at M(3, −5) and N(2, 4). Learn about the rotation transformation formula and how to apply it to points in coordinate geometry, ideal for 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