5.2.4 • GeometryHigher Tier
Enlargements (Integer Scale Factors)
The Projector — Ray Gun Mode
Phase 1 — The Anchor:Set SF = 1. The image sits exactly on the object. No change yet — build your confidence.
Scale Factor
Centre of Enlargement
Object (ABCD)
Image (A′B′C′D′)
Centre (C)
Ray Lines
🧠Logic Track
📐 Enlargement ID
Scale Factor 1 means every side of the image is 1× as long as the object, AND each image vertex is 1× as far from the centre.
📐 Property Check
Angles are preserved. A square object → square image. A triangle object → triangle image. Only lengths change.
📐 Area Ratio
Area of image = SF² × area of object. With SF = 1: area multiplies by 1×.
⚠️ Examiner Trap
The Centre of Enlargement is NOT necessarily the origin. Always locate it first — it's the starting point of every ray line. Forgetting to use the correct centre loses all method marks.
🔭 The Projector Analogy
Imagine the Centre as a projector bulb. Every ray shoots through a point on the object and extends outward. The image is where those rays land — SF × the distance from the bulb.
⚙Dynamic Solver — Select a Vertex
⚙Ray Calculator — Live Working
Point A = (2, 2) | Centre = (0, 0) | SF = 1
Step 1
Vector from Centre → A:
(2 − 0, 2 − 0) = (2, 2)
Step 2
Multiply vector by Scale Factor 1:
1 × (2, 2) = (2, 2)
Step 3
Add scaled vector to Centre:
(0 + 2, 0 + 2) = (2, 2)
✓Image A′ = (2, 2)
📊 All Image Vertices — Live Table
| Vertex | Object | Vector × SF | Image |
|---|---|---|---|
| A | (2, 2) | (2,2) × 1 = (2,2) | (2, 2) |
| B | (4, 2) | (4,2) × 1 = (4,2) | (4, 2) |
| C | (4, 4) | (4,4) × 1 = (4,4) | (4, 4) |
| D | (2, 4) | (2,4) × 1 = (2,4) | (2, 4) |
⚓ Phase 1 — Anchor
Set SF = 1 with Origin as centre. The image overlaps the object perfectly. Confirm: every ray goes from C through A and ends at A′ = A.
🔀 Phase 2 — Twist
Change SF to 2, then 3. Watch each vertex march twice or three times as far along its ray. The shape stays similar — same angles, bigger sides.
💀 Phase 3 — Killer
Shift the Centre to (1,1) or (5,5) with SF = 2. Notice the image translates as well as scales. The centre is the anchor of the whole enlargement.
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