1. What is Slope After Rotation?

The slope after rotation formula calculates how the slope of a line changes when the line is rotated by a specified angle θ (in radians) about the origin. This is useful in geometry, computer graphics, and physics applications.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

• \( Slope \) — Original slope of the line (y₂-y₁)/(x₂-x₁)
• \( \theta \) — Angle of rotation in radians
• \( Slope' \) — New slope after rotation

Explanation: The formula accounts for how both the x and y components of the line's direction vector change when rotated by angle θ.

3. Importance of Slope Calculation

Details: Understanding how slopes change under rotation is crucial in computer graphics for object transformations, in physics for analyzing vector fields, and in engineering for structural calculations.

4. Using the Calculator

Tips: Enter the coordinates of two points that define your line and the rotation angle in radians. The calculator will show both the original slope and the slope after rotation.

5. Frequently Asked Questions (FAQ)

Q1: What happens when rotating a vertical line?
A: A vertical line has undefined slope, and rotation typically results in another vertical line (undefined slope) unless rotated by exactly 90° or 270°.

Q2: How do I convert degrees to radians?
A: Multiply degrees by π/180. Many calculators have a degree-to-radian conversion function.

Q3: Does the rotation preserve the line's position?
A: This formula calculates slope change assuming rotation about the origin. The actual line position will change unless it passes through the origin.

Q4: What's the difference between positive and negative rotation?
A: Positive θ represents counterclockwise rotation, negative θ represents clockwise rotation.

Q5: Can I use this for 3D rotations?
A: No, this formula is only for 2D rotations. 3D rotations require matrix transformations.