Scale drawing worksheet with geometric shapes for calculating scale ratios.

Let's solve each of the scale drawing problems step by step. The goal is to determine the scale ratio between the original figure and its scaled image.

We will compare corresponding lengths in both figures and express the scale as a ratio (e.g., 1:2 or 2:1), where:

- 1 : x means the original is larger than the image (reduced),
- x : 1 means the image is larger than the original (enlarged).

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Problem 1: Diamond (Square rotated)

- Left shape (ABCD): Count the grid units.
- From A to B: 4 units
- So, side length = 4 cm (assuming 1 grid = 1 cm)
- Right shape (A'B'C'D'):
- From A' to B': 2 units
- Side length = 2 cm

Scale ratio:
$$
\frac{\text{Original}}{\text{Image}} = \frac{4}{2} = 2 \Rightarrow \boxed{1:2}
$$

> ✔ Answer: 1 : 2

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Problem 2: Arrow-shaped figure (PQRST → P'Q'R'S'T')

- Original (PQRST):
- PQ = 3 units
- QR = 1 unit (diagonal)
- But let’s use horizontal/vertical sides.
- PT = 3 units
- QS = 2 units
- But better: measure the rectangle part.
- PQ = 3 units, QT = 2 units (height)

- Image (P'Q'R'S'T'):
- P'Q' = 6 units
- Q'R' = 2 units
- T'S' = 4 units

So, the image is twice as big in all dimensions.

For example:
- PQ = 3 → P'Q' = 6 ⇒ ratio = 6 / 3 = 2

So, the image is double the size.

Therefore, scale ratio:
$$
\text{Original : Image} = 1 : 2
$$

But wait — the image is bigger, so the scale factor from original to image is 2:1.

But the question asks for drawing scale, meaning how the original relates to the image.

So if the original is smaller, then the scale is 1 : 2? Wait — no.

Wait: Let's clarify.

If the original is smaller, and the drawing is larger, then the scale is 1 : 2, meaning 1 unit on original = 2 units on drawing.

But here, the left figure is smaller, right one is larger, so it's an enlargement.

Thus, scale ratio (original : drawing) = 1 : 2

But look at the blank: It says "□ : □" — we need to fill the ratio.

So:

$$
\text{Original} : \text{Drawing} = 3 : 6 = 1 : 2
$$

✔ Answer: 1 : 2

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Problem 3: Triangle (STU → S'T'U')

- Original triangle STU:
- Base SU = 4 units
- Height = 3 units (from U to top)

- Image triangle S'T'U':
- Base S'U' = 2 units
- Height = 1.5 units

So, image is smaller.

Ratio of original to image:
- 4 / 2 = 2
- 3 / 1.5 = 2

So, original is twice the image ⇒ scale = 2:1

But again, the drawing (right) is smaller, so the scale is 1 : 0.5, but we write it as a whole number ratio.

Better:
Scale ratio = Original : Drawing = 2 : 1

But since the drawing is smaller, the scale is 1 : 0.5, which simplifies to 2 : 1.

Wait — standard scale notation:

- If the drawing is smaller, then the scale is 1 : x, where x > 1, meaning 1 unit on real object = x units on drawing? No.

Actually, in scale drawings, the format is:

> Scale = Drawing : Actual

But in this case, the left is the actual, and the right is the drawing?

The problem says: "Determine the drawing scale / ratio of the pair of images"

It doesn't specify which is original.

But usually, the left is the original, and the right is the scaled version.

So, left is original, right is drawing.

So:

- Original: STU → base = 4 units
- Drawing: S'T'U' → base = 2 units

So, drawing is half the size.

So, scale = Drawing : Original = 2 : 4 = 1 : 2

So, 1 : 2

Wait — but the drawing is smaller, so 1 unit on drawing = 2 units on original

So, scale is 1 : 2

Yes.

✔ Answer: 1 : 2

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Problem 4: Trapezoid (WXYZ → W'X'Y'Z')

Given measurements:

- Original:
- WX = 1 cm
- Height = 1 cm
- Image:
- W'X' = 0.5 cm
- Height = 0.5 cm

So, image is half the size.

So, drawing (image) : original = 0.5 : 1 = 1 : 2

So, scale ratio is 1 : 2

✔ Answer: 1 : 2

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Problem 5: Rectangle (MNPQ → M'N'P'O')

Given:

- Original rectangle:
- MN = 8 cm
- NO = 3 cm
- Drawing:
- M'N' = 24 cm
- N'O' = 9 cm

Now, check ratio:

- 24 / 8 = 3
- 9 / 3 = 3

So, drawing is 3 times larger.

So, scale ratio = Drawing : Original = 3 : 1

But the blank is: □ : □

So, we write 3 : 1

✔ Answer: 3 : 1

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✔ Final Answers:

| Problem | Scale Ratio |
|--------|-------------|
| 1 | 1 : 2 |
| 2 | 1 : 2 |
| 3 | 1 : 2 |
| 4 | 1 : 2 |
| 5 | 3 : 1 |

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✔ Summary:

1. 1 : 2
2. 1 : 2
3. 1 : 2
4. 1 : 2
5. 3 : 1

All based on comparing corresponding lengths and writing the ratio as Drawing : Original, assuming the left is original, right is drawing.

Let me know if you want the explanation with diagrams or measurements!