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Grade 4 · Symmetry

Trail-map design: reflect a design across a vertical line

A triangular design for a trail-map workshop places its marked vertex 3 units left of a vertical mirror line and uses height 5. Change the controls and explain what the animation reveals.

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

Watch the relationship

Paused
Trail-map design: reflect a design across a vertical line. Original x coordinate: -3. Moving image x coordinate: -3. Final image x coordinate: 3Mirror distance: 3 units on each sideAt the end, matching points have equal mirror distances.
The vertical dashed line is the mirror x = 0. Only the final image is the reflection; intermediate frames illustrate the correspondence rather than a rigid physical reflection motion.

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.

Original x coordinate
-3
Moving image x coordinate
-3
Final image x coordinate
3

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 triangular design for a trail-map workshop places its marked vertex 3 units left of a vertical mirror line and uses height 5. A reflection puts each image point on the opposite side of the mirror at the same perpendicular distance. It preserves lengths and shape while reversing orientation. The marked vertex moves from x = −3 to x = 3. Its vertical coordinate stays the same at the final image.

A relationship to keep

Reflection across x = 0: (x, y) → (−x, y)

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

  1. STEP 1

    Read the starting situation

    A triangular design for a trail-map workshop places its marked vertex 3 units left of a vertical mirror line and uses height 5. Identify what each number measures before changing a control; the worked example refers to these starting values.

  2. STEP 2

    Follow the mathematical change

    Follow the moving triangle toward the outlined image. Compare the marked vertex's distance from the mirror before and after the motion. Pause on an intermediate frame and compare the picture with the live readouts.

  3. STEP 3

    Explain and test the relationship

    The marked vertex moves from x = −3 to x = 3. Its vertical coordinate stays the same at the final image. Change one input, predict its effect, and test whether the same relationship still works.

Your turn to explain

Make a prediction. Test your reasoning.

Trail-map design: use the original situation. A triangular design for a trail-map workshop places its marked vertex 3 units left of a vertical mirror line and uses height 5. How far apart are the original marked vertex and its final reflected image?

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

Compare your explanation

6 units: 3 to reach the mirror plus another 3 on the other side.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 4 · Geometry

Find lines of reflection symmetry

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