Rotate Triangle 90 Degrees Calculator

Use this calculator to rotate a triangle 90 degrees around a specified point. Enter the original coordinates of the triangle's vertices and select the rotation direction to find the new positions after rotation.

How to Use This Calculator

To rotate a triangle 90 degrees:

Enter the coordinates of the three vertices of your triangle in the input fields labeled "Vertex A", "Vertex B", and "Vertex C".
Select the rotation direction (clockwise or counter-clockwise) from the dropdown menu.
Click the "Calculate" button to perform the rotation.
The calculator will display the new coordinates of the triangle's vertices after rotation.
You can also view a visualization of the rotated triangle using the chart below the results.

The calculator uses standard rotation formulas to transform the coordinates of each vertex. The rotation is performed around the origin (0,0) by default, but you can specify a different center point if needed.

Formula Explained

To rotate a point (x, y) 90 degrees around the origin (0,0), we use the following formulas:

For clockwise rotation: x' = y y' = -x For counter-clockwise rotation: x' = -y y' = x

Where (x', y') are the new coordinates after rotation. These formulas effectively swap and negate the coordinates to achieve a 90-degree rotation.

For rotation around a different center point (a, b), we first translate the point to the origin, perform the rotation, and then translate back:

Translate to origin: x_temp = x - a y_temp = y - b Rotate: x_rotated = y_temp (for clockwise) or -y_temp (for counter-clockwise) y_rotated = -x_temp (for clockwise) or x_temp (for counter-clockwise) Translate back: x' = x_rotated + a y' = y_rotated + b

Worked Example

Let's rotate the triangle with vertices at (1, 2), (3, 4), and (5, 6) 90 degrees clockwise around the origin (0,0).

Using the formulas:

For vertex (1, 2):
- x' = y = 2
- y' = -x = -1
- New coordinates: (2, -1)
For vertex (3, 4):
- x' = y = 4
- y' = -x = -3
- New coordinates: (4, -3)
For vertex (5, 6):
- x' = y = 6
- y' = -x = -5
- New coordinates: (6, -5)

The rotated triangle will have vertices at (2, -1), (4, -3), and (6, -5).

Frequently Asked Questions

Can I rotate a triangle around a different point?: Yes, the calculator allows you to specify a different center point for rotation. Simply enter the coordinates of the center point in the provided fields.
What happens if I enter non-numeric values?: The calculator will display an error message if you enter non-numeric values. Please ensure all inputs are valid numbers.
Can I rotate a triangle by a different angle?: This calculator specifically handles 90-degree rotations. For other angles, you would need a different calculator or mathematical approach.
Is the rotation direction important?: Yes, the direction of rotation (clockwise or counter-clockwise) affects the final position of the rotated triangle. Make sure to select the correct direction for your needs.