The coordinate lab
Drag a blue vertex; coordinates snap to integers. Or edit coordinates below. The grid fits both figures automatically.
Investigation missions
Choose a mission to set up the lab. Predict first, reveal the image, and record evidence. Return here to compare your findings.
Discuss with a partner
How can a shape turn while its vertex order stays the same? Why does reflection reverse that order? When does a dilation create a congruent image?
Coordinate challenge
Work without the lab first. All rotations and dilations use the origin.
Your transformation rule book
Orientation: two useful meanings
A rotation changes the direction a figure faces, but preserves the clockwise or counterclockwise order of its labeled vertices. A reflection reverses this vertex order. Translations and positive dilations preserve vertex order.
Congruent or similar?
Translations, reflections, and rotations preserve lengths and angles, so the image is congruent to the preimage. A positive dilation preserves angles and multiplies every length by k. The figures are similar; they are congruent only when k = 1. Area is multiplied by k².
Teacher notes
8.3A: corresponding side ratios; 8.3B: compare attributes of dilated figures; 8.3C: coordinate dilation rules. 8.10A: orientation and congruence; 8.10B: congruence-preserving transformations; 8.10C: algebraic rules for translations, axis reflections, and quarter-turn rotations. Area comparisons extend to 8.10D.