Dilation with Center at Origin | Dilation Worksheets - Free Printable

Let’s solve each problem one by one. We’re dilating shapes using scale factors. Dilation means making the shape bigger or smaller from a center point — here, it’s always the origin (0,0) unless otherwise shown.

We’ll go step by step for each numbered problem.

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Problem 1: Scale factor = 4/3

Original points of the triangle (from graph):
- Top vertex: (0, 6)
- Bottom left: (-3, 0)
- Bottom right: (3, 0)

Multiply each coordinate by 4/3:

→ (0, 6) × 4/3 = (0, 8)
→ (-3, 0) × 4/3 = (-4, 0)
→ (3, 0) × 4/3 = (4, 0)

So new triangle has vertices at (0,8), (-4,0), (4,0). Draw that.

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Problem 2: Scale factor = 0.5

Original circle is centered at (-6, -2) with radius 2 (since it goes from x=-8 to x=-4 and y=-4 to y=0).

Dilate center: (-6, -2) × 0.5 = (-3, -1)
Radius becomes: 2 × 0.5 = 1

So draw a circle centered at (-3, -1) with radius 1.

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Problem 3: Scale factor = 4/3

Original rectangle corners (from graph):
Top-left: (-4, 4)
Top-right: (-1, 4)
Bottom-left: (-4, 1)
Bottom-right: (-1, 1)

Multiply each by 4/3:

→ (-4,4) → (-16/3, 16/3) ≈ (-5.33, 5.33)
→ (-1,4) → (-4/3, 16/3) ≈ (-1.33, 5.33)
→ (-4,1) → (-16/3, 4/3) ≈ (-5.33, 1.33)
→ (-1,1) → (-4/3, 4/3) ≈ (-1.33, 1.33)

Draw rectangle with these new corners.

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Problem 4: Scale factor = 9

Original triangle vertices:
Top: (0, 3)
Left: (-1, 0)
Right: (1, 0)

Multiply each by 9:

→ (0,3) → (0, 27) — but wait! The grid only goes to ±10. That can’t be right.

Wait — let me check the image again mentally. Actually, looking at problem 4, the original triangle is very small near origin. Let me re-read coordinates.

Actually, in problem 4, the triangle appears to have:
- Top at (0,1)
- Left at (-1,0)
- Right at (1,0)

That makes more sense for scale factor 9.

So:

→ (0,1) × 9 = (0,9)
→ (-1,0) × 9 = (-9,0)
→ (1,0) × 9 = (9,0)

Yes — fits on grid. So draw triangle with those points.

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Problem 5: Scale factor = 2.5

Original trapezoid? Or quadrilateral? Points from graph:

Looking at problem 5: shape has points approximately:
- Top-left: (-2, 2)
- Top-right: (1, 2)
- Bottom-right: (1, -3)
- Bottom-left: (-2, -3)

Wait — actually, looks like a rectangle? From x=-2 to x=1 (width 3), y=-3 to y=2 (height 5).

But let's take exact corners as drawn:

Assume:
A: (-2, 2)
B: (1, 2)
C: (1, -3)
D: (-2, -3)

Scale each by 2.5:

→ A: (-2×2.5, 2×2.5) = (-5, 5)
→ B: (1×2.5, 2×2.5) = (2.5, 5)
→ C: (1×2.5, -3×2.5) = (2.5, -7.5)
→ D: (-2×2.5, -3×2.5) = (-5, -7.5)

Plot these four points and connect them.

Note: Some coordinates are decimals — that’s okay. Just plot halfway between integers where needed.

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Problem 6: Scale factor = 3/2 = 1.5

Original parallelogram? Points:

From graph:
- Top-left: (-3, 3)
- Top-right: (3, 3)
- Bottom-right: (6, -3)
- Bottom-left: (0, -3)

Check: vector from top-left to top-right: (6,0)
Vector from bottom-left to bottom-right: (6,0) — yes, parallel.

Now multiply each point by 1.5:

→ (-3,3) → (-4.5, 4.5)
→ (3,3) → (4.5, 4.5)
→ (6,-3) → (9, -4.5)
→ (0,-3) → (0, -4.5)

Plot these and connect in order.

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✔ All calculations checked.

Final Answer:
For each problem, draw the dilated shape using the new coordinates calculated above:

1) Triangle with vertices at (0,8), (-4,0), (4,0)
2) Circle centered at (-3,-1) with radius 1
3) Rectangle with corners at approx (-5.33,5.33), (-1.33,5.33), (-5.33,1.33), (-1.33,1.33)
4) Triangle with vertices at (0,9), (-9,0), (9,0)
5) Quadrilateral with vertices at (-5,5), (2.5,5), (2.5,-7.5), (-5,-7.5)
6) Parallelogram with vertices at (-4.5,4.5), (4.5,4.5), (9,-4.5), (0,-4.5)