Move it. Turn it. Grow it.

SparkClass

Build a sequence and watch exactly what changes—and what stays the same.

CCSS 8.G.A.1–A.4
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x, y: −8 … 8
Original figure and transformed image on a coordinate plane The original triangle is gray. Its transformed image is coral. Mathematical y values increase upward.
Live

Try a transformation. The gray original stays fixed while the coral image updates.

Congruent
Coordinate Rule(x, y) → (x + 2, y + 1)
A → A′
Sequence Builder0 / 5 Steps

Load A Sequence Preset

No steps yet. Adjust the rule above, then add it to begin.

Vertex CoordinatesLive Mapping

Coordinates are read as (x, y). Decimal values are rounded to 2 places for display.

Teacher notes · making the math visible

Move from prediction to evidence: students name the rule, predict the coordinates, then use the plane and table to check.

1

Start with one rule

Use the default A(1, 1), B(4, 1), C(2, 3). Before moving a slider, ask for the coordinates of A′. In rotation mode, emphasize that positive angles turn counterclockwise and that the center is the origin.

2

Make order matter

Build “translate, then reflect” and ask whether reversing the two steps gives the same final image. Click any numbered step to inspect its intermediate image. The coordinate columns show that each rule uses the previous image—not the original again.

3

Separate congruence from similarity

Compare a rigid sequence with “rotate, then dilate.” For a non-unit dilation, angle measures and parallelism survive, but lengths do not. Test k = 1 (identity) and k = −1 (a 180° rotation about the origin): both special cases are congruent.

4

Ask for a precise invariant claim

Have students complete: “This image is ___ to the original because ___ is preserved and ___ changes.” Avoid using “same shape” as a synonym for congruent; congruent figures must also have the same size.

CCSS alignment:
  • 8.G.A.1: verify experimentally that rigid transformations preserve lengths, angles, lines, and parallel lines.
  • 8.G.A.2: describe a sequence of rigid moves that shows two figures are congruent.
  • 8.G.A.3: describe the effects of translations, rotations, reflections, and dilations using coordinates.
  • 8.G.A.4: use a sequence that includes a dilation to explain similarity.