Rotation 270 Degrees About the Origin Calculator

Rotate points around the origin with instant verification. Check coordinates, matrices, and downloadable records easily. Practice transformations confidently using structured steps and reliable outputs.

Calculator

Single Point X

Single Point Y

Decimal Places

Output Notation

Reference Mode

Auto Label Prefix

Batch Coordinates

If batch coordinates are provided, they will be used instead of the single-point inputs.

Show steps section

Show graph after calculation

Reset

Example Data Table

Label	Original Point	Rule Applied	Rotated Point
A	(2, 3)	(x, y) → (y, -x)	(3, -2)
B	(-4, 1)	(x, y) → (y, -x)	(1, 4)
C	(0, -5)	(x, y) → (y, -x)	(-5, 0)
D	(6, 0)	(x, y) → (y, -x)	(0, -6)

Formula Used

A 270-degree rotation about the origin is usually taken counterclockwise. It matches a 90-degree clockwise turn.

Coordinate rule: (x, y) → (y, -x)

Matrix form:

[ 0 1 ]
[ -1 0 ]

The distance from the origin stays unchanged because rotation is a rigid transformation. The determinant is 1, so orientation is preserved.

How to Use This Calculator

Enter one point using the x and y fields, or paste several points into the batch area.
Choose the number of decimal places you want in the output.
Select your preferred notation style for the result display.
Choose the reference wording: 270° counterclockwise or 90° clockwise equivalent.
Enable the graph option if you want a plotted comparison.
Press Calculate Rotation to view results above the form.
Download the result table as CSV or PDF if needed.

FAQs

1. What is the rule for rotating 270 degrees about the origin?

The coordinate rule is (x, y) → (y, -x). The old y-value becomes the new x-value, and the negative old x-value becomes the new y-value.

2. Is 270 degrees counterclockwise the same as 90 degrees clockwise?

Yes. A 270-degree counterclockwise rotation lands at the same final position as a 90-degree clockwise rotation, so both produce identical rotated coordinates.

3. Does rotation change the distance from the origin?

No. Rotation preserves distance from the origin. The point changes direction, but its radius remains the same after the transformation.

4. Can I calculate more than one point at once?

Yes. Use the batch coordinates box and enter one point per line. You can write x,y or label,x,y for each row.

5. What happens to points on the axes?

Axis points stay the same distance from the origin but move to another axis position unless the point is the origin itself. The origin remains unchanged.

6. Why does the calculator show a matrix?

The matrix gives the formal linear transformation for the rotation. It is useful in coordinate geometry, linear algebra, and repeated transformation work.

7. Can I export the rotated results?

Yes. After calculation, you can download the result table as CSV or PDF. This helps with reports, homework checking, or saved reference work.

8. Does the graph help verify the answer?

Yes. The graph places original and rotated points on the same coordinate plane, making it easier to confirm direction, position, and symmetry visually.