Slide it. Flip it. Turn it. Scale it. Discover what stays the same.
Your mission Use coordinate rules to predict images and explain congruence, orientation, and similarity. TEKS 8.3 A–C • 8.10 A–C • Area extension: 8.10D
The coordinate lab
● Pre-image◆ Final image
Coordinates
Edit the pre-image x and y values (−8 to 8). Press Tab to apply. The graph updates beside you.
Final image coordinates stay hidden until Reveal image. Enter your prediction in the right panel.
Drag a blue vertex; coordinates snap to integers. Or select Coordinates to edit. 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
Which transformations change the direction a figure faces? Which preserve its size and corresponding angles? 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 and angles
Orientation here means facing direction. Translation and positive dilation keep the same orientation; rotation turns the figure, and reflection makes a mirror image. Corresponding angles of the final image are congruent to those of the pre-image in all four transformations.
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.