Coordinate Transformation Calculator
Reflect, rotate or translate a point in the coordinate plane. Keep exact fractional coordinates and compare the original point with its image on equal-scale axes.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Apply the coordinate rule for the selected transformation. A reflection changes the coordinate perpendicular to its mirror, a right-angle rotation swaps and changes signs, and translation adds the displacement to each coordinate.
Reflect x-axis: (x,−y); reflect y-axis: (−x,y); rotate 90° CCW: (−y,x); translate: (x+dx,y+dy)
Worked example
Point (3,2) reflected across the x-axis becomes (3,−2). Rotated 90° counterclockwise about the origin it becomes (−2,3). Translating by (2,−1) gives (5,1).
Assumptions and input details
Rotations and origin symmetry are centered at (0,0). Positive rotation is counterclockwise. Inputs accept fractions and decimals with up to six places, magnitudes at most 1e6 and reduced denominators at most 1e6. A is the original point and B is its image; the connecting segment compares positions and is not the rotation path. The diagram and displacement length are approximate; fractional output coordinates are exact.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Transformed coordinates use exact fraction arithmetic; plotted positions and the straight-line displacement are approximate.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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