Transform a polygon by translation, reflection, rotation or dilation. The calculator plots the original shape and its image on the same equal-scale grid, lists corresponding coordinates, and creates a practice worksheet with a separate answer key.
(x, y) → (x + (-5), y + (-2))
A (1, 1); B (4, 1); C (2, 4)
A′ (-4, -1)
B′ (-1, -1)
C′ (-3, 2)
Side lengths and angle measures are preserved.
| Vertex | Original X | Original Y | Image X | Image Y |
|---|---|---|---|---|
| A | 1 | 1 | -4 | -1 |
| B | 4 | 1 | -1 | -1 |
| C | 2 | 4 | -3 | 2 |
One transformation at a time. Equal X/Y units, automatic range including every vertex. Original: solid blue; image: dashed orange. Overlapping vertices may overlap labels; the table preserves every coordinate.
PDF includes the problem and space to work. Practice mode can add a separate answer key; Explore mode gives a worked page.
SVG and PNG match the diagram currently shown. CSV includes calculated values, even in practice mode.
Practice PDF page 1 keeps the answers hidden, even after revealing them on screen. PDF pages use high-resolution images.
The original triangle has A (1, 1), B (4, 1) and C (2, 4). Translate it 5 units left and 2 units down: (x, y) → (x − 5, y − 2).
The image is A′ (−4, −1), B′ (−1, −1) and C′ (−3, 2). Each corresponding pair has the same horizontal and vertical change. The triangle keeps its size and shape. The prime mark distinguishes an image vertex from its original.
Free for class, homework and presentations. Two-page PDFs: question first, answer key second. Print in portrait at 100% / Actual size.
Translation adds the same horizontal and vertical shift to every point. Reflection in the x-axis changes (x, y) to (x, −y); reflection in the y-axis changes it to (−x, y). The diagonal options swap coordinates for y = x, or negate and swap them for y = −x. A dashed reference line identifies the mirror.
About the origin, 90° anticlockwise maps (x, y) to (−y, x); 180° maps it to (−x, −y); and 270° anticlockwise maps it to (y, −x). For another centre, subtract that centre, rotate the relative coordinates, then add it back. Here 270° anticlockwise is also labelled 90° clockwise.
For centre (h, k) and positive scale factor s, the new point is (h + s(x − h), k + s(y − k)). Side lengths multiply by s and area by s². Factors from 0.1 to 5 are supported; a factor below 1 reduces the shape. Translations, reflections and rotations preserve side lengths.
Use a simple polygon with 3–6 distinct vertices entered around its perimeter. Zero-area and crossing shapes are rejected. Input and output coordinates must stay within −50 to 50. This tool applies one transformation at a time, with no matrix input or automatic composition. A4/Letter PDFs use a separate answer page; CSV includes original and image coordinates.
Further reference: GeoGebra manual: transformation tools. Examples, tool design and practice sheets on this page are original ChartsAI work; no affiliation is implied.
Yes. Enter Centre X and Centre Y for rotation or dilation. A small cross marks the centre on the diagram. Rotation angles are limited to quarter, half and three-quarter turns.
This version supports the x-axis, y-axis, y = x and y = −x. An arbitrary line or a function transformation is outside this tool’s scope.
The range automatically includes every original and transformed vertex and the selected centre. X and Y units remain equal. A result beyond −50 to 50 produces an error rather than hiding a vertex.
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Start with coordinate-plane plotting practice, or browse all free math tools.