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Grade 7 · Similarity

Architect's sketch: Compare map and model scales

Architect's sketch investigation: compare map and model scales. 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
Architect's sketch: Compare map and model scales. Current length multiplier: 1. Current width: 4.5. Current area: 16.875. Final area multiplier: 5.063One length multiplier, two changing dimensionsOriginal dimensions: 4.5 by 3.75Current k = 1; area = 16.875Dashed: original · solid: dilated image
Only positive uniform dilations are shown. The axis drawing scale is equal horizontally and vertically and remains fixed during playback. The dashed original and solid image share the lower-left corner as dilation center.

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 length multiplier
1
Current width
4.5
Current area
16.875
Final area multiplier
5.063

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 dilation multiplies every length by the same positive factor. Ratios of corresponding sides stay equal, but area changes by the square of that factor because two independent dimensions both change. A scale below one shrinks the figure without changing its shape. This investigation begins with original width = 4.5; original height = 3.75; length scale factor k = 2.25. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.

A relationship to keep

new lengths = k × old lengths; new area = k² × old area

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

    Compare the original rectangle with its image, matching width to width and height to height.

  2. STEP 2

    Follow the changing model

    Playback changes the common scale factor from one to the chosen k while keeping the dilation center fixed.

  3. STEP 3

    Check and explain the relationship

    Divide corresponding lengths to recover k and corresponding areas to recover k².

Your turn to explain

Make a prediction. Test your reasoning.

Architect's sketch: Dilate a 4.5-by-3.75 rectangle by length factor 2.25. Find its final area.

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

Compare your explanation

85.43 square units; the original area 16.875 is multiplied by 5.063.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 7 · Geometry

Convert a map length with a scale

A map scale relates drawing length and actual length through consistent units.