Transformation coordinates explorer

This tool moves a shape on the coordinate plane and lists the new coordinates of every vertex. It helps students who understand the idea of a transformation but make slips when they calculate the image points.

How do I use it?

1. Type 3 to 8 vertices as x,y pairs, in order around the shape.
2. Choose a first transformation and fill in its numbers.
3. Optionally choose a second transformation to compare the order.
4. Press “Transform” and read the table and the plot.

How does it work?

The x-axis points right, the y-axis points up, and anticlockwise is positive. Each rule is applied to every vertex, and the rule used is written out above the table.

• Translation by (h, k) sends (x, y) to (x + h, y + k).
• Reflection uses the x-axis, the y-axis, y = x, y = −x, or a line x = c or y = c.
• Rotation is in multiples of 90° about a centre you choose, origin by default.
• Enlargement sends each point to centre + k × (point − centre).

With two transformations, the tool also shows the vertices when they are done in the opposite order and states whether the images match.

A short worked example

The default shape has vertices A(1, 0), B(3, 0) and C(3, 2). Rotate it 90° anticlockwise about the origin.

The rule is (x, y) → (−y, x). So A(1, 0) goes to (0, 1), B(3, 0) goes to (0, 3) and C(3, 2) goes to (−2, 3).

Change the angle to 180° and A goes to (−1, 0). Change the enlargement factor to 1 and the image sits exactly on the original.

What are its limits?

The tool shows coordinates and a sketch, so it cannot replace accurate construction with a ruler, compass or protractor. Rotations are limited to multiples of 90°. It does not check a description you write in words, so you still need to state the full transformation in your answer.

Where does it connect to the lessons?

The tool supports congruency, enlargement and combined transformations. Its practice questions are a good place to test your coordinates against the table here.

If you want a teacher to trace where your points go wrong, SPM Mathematics tuition is built for that. It begins with the one-hour trial class (from RM50).