To rotate a point \((-4, 1)\) 270 degrees counterclockwise around the origin, we can use the standard rotation formulas.

### Rotation Formulas

When rotating a point \((x, y)\) counterclockwise about the origin:
1. **90 degrees**: \((x, y) \to (-y, x)\)
2. **180 degrees**: \((x, y) \to (-x, -y)\)
3. **270 degrees**: \((x, y) \to (y, -x)\)

### Applying the 270-Degree Rotation

Given the point \((-4, 1)\), we use the 270-degree formula:

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

Substitute \((x, y) = (-4, 1)\):

\[
(-4, 1) \to (1, -(-4))
\]

Simplifying further:

\[
(-4, 1) \to (1, 4)
\]

### Result

After rotating the point \((-4, 1)\) 270 degrees counterclockwise, the new coordinates are **(1, 4)**.

Would you like to explore more on rotations or ask something else?

### Follow-Up Questions:

1. What is the result of rotating the point (3, -2) by 90 degrees counterclockwise?
2. How do you rotate a point by 180 degrees around a different point than the origin?
3. What is the formula for rotating a point clockwise by 270 degrees?
4. How would you find the coordinates of a point after rotating it 45 degrees?
5. What happens if you rotate a point (x, y) by 360 degrees?

**Tip**: For clockwise rotations, use the counterclockwise formulas with negative angles or adjust accordingly!

Explore how to rotate the point (-4, 1) 270 degrees counterclockwise around the origin using rotation formulas in the coordinate plane. Understand the step-by-step process and check the final coordinates after rotation. Suitable for high school 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