Coordinates · interactive lab
Transformation playground
Translate, rotate, reflect, or scale a triangle and compare its coordinates and area.
Transformation playgroundLIVE EXPLORATION
Green: original · orange: transformed
Your measurements
The original triangle is A(−2, −1), B(2, −1), C(0, 2). Rotations and dilations are centered at the origin.
Why it works
Rotation: (x, y) → (x cos θ − y sin θ, x sin θ + y cos θ)
A little question. A clearer picture.
Transformation playground: common questions
Wondering about the why? Start here.
Which transformations keep a triangle the same size?
Translations, rotations, and reflections preserve lengths, angles, and area. A dilation changes lengths by its scale factor while preserving angles. In this playground, rotations and dilations are centered at the origin.
Learn the transformation rulesWhy does doubling a shape’s size quadruple its area?
A dilation by a positive factor k multiplies each length by k, so area is multiplied by k². Doubling every length makes the area four times as large; halving every length makes it one quarter as large.
Explore similarity and scale