Mrs.D Math · 8th Grade

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Geometry · Dilations, Perimeter & Area
🔍 Dilation
📏 Scale Factor k
📐 Perimeter & Area
🖼️ 4×6 → 12×18
📏 P′ = P · k
🔶 A′ = A · k²
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📚 Dilations & Measurements

What Is a Dilation?

A dilation makes a figure bigger or smaller using a scale factor k. Every side length gets multiplied by k.

1
From the video: a 4″ × 6″ photo dilated by k = 3
4 × 3 = 12    6 × 3 = 18  →  12″ × 18″
2
Perimeter changes by k: P′ = P · k
P = 20″  →  P′ = 20 × 3 = 60″
3
Area changes by k²: A′ = A · k²
A = 24 sq in  →  A′ = 24 × 3² = 24 × 9 = 216 sq in

Why k² for Area?

Area = length × width. BOTH sides get multiplied by k, so the area gets multiplied by k × k = k²!

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A′ = (l · k)(w · k) = l · w · k²
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Going backwards? k = new perimeter ÷ old perimeter

How to Play

📏
What is the Perimeter — Find new perimeters (and scale factors) after a dilation.
🔶
What is the Area — Find new areas using k².
🆕
Mixed — Both together for the ultimate challenge!
🧮
Calculator — New this year! Tap the gold button, bottom-left. Try it in your head first — then verify! 💡
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