Geometric Transformations: Move, Flip and Turn
Understand that translations, reflections and rotations keep a shape congruent while a dilation makes it similar, scaling lengths by k and area by k squared, each with its own coordinate rule.
Before you try
What if you doubled every side of a shape? Would its area double too?
Try it out
Interactive activity
Sign in to play
Use a Google account (yours or a parent’s) to unlock this simulator. We store only your name and email so your favourites and progress follow you.
Signing in needs an internet connection. Once you are signed in, simulators also work offline.
Free preview
Loading controls…
What happened?
Move a control to see what changes and why.
Shapes move and resize perfectly, with no distortion. The rules shown apply to flat shapes on a grid.
Something went wrong
This simulator could not load. Check your connection and try again.
Try these ideas
- Reflect a triangle in the y axis and compare the coordinates in the table.
- Rotate 90° three times and see where the shape ends up.
- Dilate by 2 and check that the area becomes four times bigger.
Why it works
A transformation moves a shape without bending it. Translating slides every point the same way. Reflecting flips it across a mirror line and reverses the order of the corners. Rotating turns every point about the origin, keeping each one the same distance away. All three give an image that is congruent to the original: identical in size and shape, just somewhere else.
Dilating is different. It stretches every point away from the origin by a scale factor k, so all the lengths multiply by k and the area multiplies by k squared. The image is similar rather than congruent: the same shape with the same angles, at a different size. In this simulator you pick a shape and a transformation, watch the image animate across, and read the coordinate rule and both areas.
Check your understanding
Question 1 of 4
Which transformation changes the size of a shape?
What is the coordinate rule for a reflection in the y axis?
You dilate a shape by a factor of 3. What happens to its area?
Which transformation reverses the order of the labelled corners?
Explain it in your own words
What changed? Why did it happen? Where might you notice this in everyday life?
For parents & teachers
- Fold paper along a line and cut a shape to make a reflection.
- Look for rotation and reflection in rangoli patterns or tiles.
- Ask why a photocopy at 200 per cent uses four times the paper area.