This worksheet challenges students to find the scale ratio between original shapes and their scaled versions.

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).

---

Problem 1: Diamond (Square rotated)

- Left shape (ABCD): Count the grid units.
- From A to B: 4 units (diagonal), but since it's a square rotated, measure side length using grid.
- Actually, count horizontal/vertical distance: from A to B is 4 squares diagonally? Let's better use coordinates.

But we can measure the side length directly on the grid.

Looking at ABCD:
- AB goes from (say) (1,5) to (3,7) — not easy.

Better: Use diagonal or side.

Instead, observe that:
- Each small square is 1 cm × 1 cm.
- In the large diamond ABCD:
- Horizontal width = 6 cm (from leftmost to rightmost point)
- Vertical height = 6 cm
- So it's a square rotated 45° with diagonal = 6 cm
- But actually, side length can be calculated via Pythagoras.

Wait — easier: Measure the side length.

From A to B:
- A is at (1,5), B is at (3,7) → Δx = 2, Δy = 2 → Distance = √(2² + 2²) = √8 ≈ 2.83 cm

But instead of approximating, let’s count how many grid squares.

Actually, look at the grid:

- Large diamond ABCD: spans 6 units horizontally and vertically.
- The distance from A to C (diagonal) is 6 cm.
- Since it's a square rotated, diagonal = s√2 → s = 6 / √2 = 3√2 ≈ 4.24 cm

Now smaller diamond A'B'C'D':
- Spans 2 units → diagonal = 2 cm → side = 2 / √2 = √2 ≈ 1.41 cm

So scale factor = (small side)/(large side) = (√2) / (3√2) = 1/3

Thus, scale ratio = 1 : 3

✔ Answer: 1 : 3

---

Problem 2: Irregular Pentagon (PQRST and P'Q'R'S'T')

Compare dimensions.

Left figure (PQRST):
- PQ = 2 cm (horizontal)
- QR = 1 cm (up-right)
- RS = 1 cm (down)
- ST = 2 cm (left)
- TP = 1 cm (up)

But better: Compare corresponding sides.

Right figure (P'Q'R'S'T'):
- P'Q' = 4 cm
- Q'R' = 2 cm
- R'S' = 2 cm
- S'T' = 4 cm
- T'P' = 2 cm

So every dimension is double.

Scale factor = 2:1 → Original is smaller, image is larger.

So the scale is 2 : 1

But the question says: "determine the drawing scale / ratio"

Usually, scale is written as original : image

So if original is smaller, and image is twice as big → 1 : 2

Wait — check which one is original?

In problem 2, left is smaller, right is larger → so the drawing scale is 1 : 2

But let's confirm:

Original (left): PQ = 2 cm
Image (right): P'Q' = 4 cm → ratio = 2:1 → meaning image is 2× original → scale = 1 : 2

✔ Answer: 1 : 2

---

Problem 3: Triangle (STU and S'T'U')

Left triangle (STU):
- Base SU = 4 cm
- Height from T to SU = 3 cm

Right triangle (S'T'U'):
- Base S'U' = 2 cm
- Height = 1.5 cm

So scale factor = 2/4 = 0.5 → 1:2

So image is half size → scale = 1 : 2

✔ Answer: 1 : 2

---

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

Given measurements:

- Original (WXYZ):
- Top base WX = 1 cm
- Height = 1 cm
- Bottom base ZY = 1 cm (looks like isosceles trapezoid)
- Image (W'X'Y'Z'):
- Top base W'X' = 0.5 cm
- Height = 0.5 cm
- Bottom base Z'Y' = 0.5 cm

So all dimensions are halved.

Scale factor = 0.5 → so image is half size → scale = 1 : 2

But wait — is the original the bigger one?

Yes: original has 1 cm, image has 0.5 cm → so original : image = 1 : 0.5 = 2 : 1

But scale is usually expressed as original : image

So if original is 1 cm, image is 0.5 cm → scale = 2 : 1

But the question asks for the drawing scale, which is often image : original or original : image?

Standard: Scale = drawing : actual

But here, both are drawings — we need to find the ratio of the two images.

Typically, the first image is the original, second is the scaled version.

So scale = original : image = 1 cm : 0.5 cm = 2 : 1

But wait: the labels are WXYZ and W'X'Y'Z', so W'X'Y'Z' is the scaled version.

So scale ratio = original : image = 1 : 0.5 = 2 : 1 → so 2 : 1

But let's write it as 2 : 1

Alternatively, sometimes they want simplified form.

But 1 cm to 0.5 cm → ratio = 2:1

✔ Answer: 2 : 1

Wait — but in the box it says “□ : □”, so we can write 2 : 1

But let’s double-check:

Original: 1 cm
Scaled: 0.5 cm
So scaled is half → scale = 1 : 2 (if you mean scaled : original)

But standard convention: Scale = Drawing : Actual

Here, if WXYZ is the actual object, and W'X'Y'Z' is the drawing, then drawing is smaller → scale = 1 : 2

But the problem says: “determine the drawing scale / ratio of the pair”

And the first image is drawn larger — likely it's the actual size, and the second is the scaled drawing.

But in this case, both are drawings — perhaps the first is the original, second is scaled.

So scale = original : scaled = 1 cm : 0.5 cm = 2 : 1

But typically, scale ratios are written as drawing : actual, so if the second one is the drawing, then:

Drawing = 0.5 cm, Actual = 1 cm → Scale = 0.5 : 1 = 1 : 2

Ah! This is key.

If the second figure is the drawing, and the first is the actual object, then:

- Drawing size = 0.5 cm
- Actual size = 1 cm
→ Scale = 0.5 : 1 = 1 : 2

Similarly, in problem 1: large diamond is actual, small is drawing → scale = 1 : 3

So yes, scale = drawing : actual

Therefore, in problem 4:

- Drawing (W'X'Y'Z') = 0.5 cm
- Actual (WXYZ) = 1 cm
→ Scale = 0.5 : 1 = 1 : 2

✔ Answer: 1 : 2

Wait — but the image shows WXYZ on left, W'X'Y'Z' on right, and W'X'Y'Z' is smaller → so it's a reduced drawing.

So scale = drawing : actual = 0.5 : 1 = 1 : 2

✔ Answer: 1 : 2

---

Problem 5: Rectangle (MNO P and M'N'O'P')

Given:

- Small rectangle (MNPQ):
- MN = 8 cm
- NO = 3 cm

- Large rectangle (M'N'O'P'):
- M'N' = 24 cm
- N'O' = 9 cm

Check scale:

Length: 8 cm → 24 cm → 24 / 8 = 3
Width: 3 cm → 9 cm → 9 / 3 = 3

So scale factor = 3 → drawing is enlarged

So drawing : actual = 3 : 1

But which is the actual?

Again, the first one is smaller — likely the actual object, second is the drawing.

So drawing is 3 times actual → scale = 3 : 1

But if the drawing is the larger one, then scale = 3 : 1

Yes.

So scale ratio = 3 : 1

✔ Answer: 3 : 1

---

✔ Final Answers:

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

---

✔ Boxed Answers:

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

---

📌 Explanation Summary:

To find the scale ratio:
1. Identify corresponding sides in both figures.
2. Divide the measurement of the drawing by the actual (or vice versa).
3. Express as a simplified ratio.
4. Usually, scale = drawing : actual
- If drawing is smaller → e.g., 1:2
- If drawing is larger → e.g., 3:1

In these problems, the left figure is the actual object, and the right figure is the drawing, so:
- Scale = drawing : actual

That's why even when the drawing is smaller, we write 1 : x, and when larger, x : 1

---

✔ Final Answer:

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