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Grade 10 · Transformations

Workshop model: Track corresponding geometric vertices

Workshop model investigation: track corresponding geometric vertices. Change the quantities, follow the motion, and explain the result using the displayed mathematical relationship.

Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.

Watch the relationship

Paused
Workshop model: Track corresponding geometric vertices. Current displacement: (0, 0). Image of (1,1): (1, 1). Final movement length: 3.606Every vertex receives the same displacementFinal vector (-3, -2) · grid step 2Image of (1,1): (1, 1)
The plot uses equal horizontal and vertical units, centered on the origin. Only a translation is performed, with no rotation, reflection, or change of size. Inputs and movement components may be negative.

Starts paused. Play once, pause anywhere, or use Step to inspect the mathematics. Playback stops when this panel leaves the screen.

Make it your experiment

Change one value. Notice what follows.

The controls adjust the model. Numbers below describe the current frame. Decimals are rounded.

Current displacement
(0, 0)
Image of (1,1)
(1, 1)
Final movement length
3.606

HD animation studio

From experiment to screen.

Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.

Understand what you are seeing

The idea behind the motion.

A translation adds one displacement vector to every point of a figure. Corresponding sides remain parallel and equal, so shape and size are preserved. The movement's length comes from its horizontal and vertical components, not from adding those components directly. This investigation begins with horizontal displacement = -3; vertical displacement = -2. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.

A relationship to keep

(x,y) ↦ (x+u,y+v)

Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.

  1. STEP 1

    Represent the given quantities

    Start with triangle vertices (1,1), (3,1), and (1,3), and read the displacement components in order.

  2. STEP 2

    Follow the changing model

    Playback adds the same partial displacement to every vertex; the dashed outline keeps the original visible.

  3. STEP 3

    Check and explain the relationship

    Check the image of (1,1), then compare corresponding edge lengths to verify that translation preserves distances.

Your turn to explain

Make a prediction. Test your reasoning.

Workshop model: Translate (1,1) by (-3,-2). Find the image and movement length.

Use the values specified in the question. Reset restores the initial values for this investigation.

Compare your explanation

The image is (-2,-1); movement length is √(13) ≈ 3.606.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 10 · Geometry

Prove a quadrilateral is a parallelogram with midpoints

Use diagonal bisection as a coordinate criterion.