SOLVED: Dilations/Translations Worksheet 1. In Math, the word ... - Free Printable

Let's solve the Dilations/Translations Worksheet step by step.

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1. In math, the word dilate means to ________ or ________ a figure.

✔ Answer:
Enlargen or shrink
*(Dilation means to enlarge or reduce a figure proportionally from a center point.)*

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2. If a scale factor is less than 1, then your figure gets ________.

✔ Answer:
Smaller
*(A scale factor between 0 and 1 reduces the size of the figure.)*

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3. If a scale factor is greater than 1, then your figure gets ________.

✔ Answer:
Larger
*(A scale factor greater than 1 enlarges the figure.)*

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4. Graph the dilated image of triangle JKL using a scale factor of 2 and (0,0) as the center of dilation.

We need to find the coordinates of the original triangle JKL, then apply a scale factor of 2 with the origin (0,0) as the center of dilation.

#### Step 1: Find coordinates of original points from the graph:

From the grid:
- J: (2, 4)
- K: (1, 1)
- L: (5, 1)

#### Step 2: Apply dilation formula:

When dilating about the origin with scale factor $ k $, the rule is:
$$
(x, y) \rightarrow (kx, ky)
$$

Here, $ k = 2 $

So:
- $ J(2, 4) \rightarrow J'(2 \cdot 2, 2 \cdot 4) = (4, 8) $
- $ K(1, 1) \rightarrow K'(2 \cdot 1, 2 \cdot 1) = (2, 2) $
- $ L(5, 1) \rightarrow L'(2 \cdot 5, 2 \cdot 1) = (10, 2) $

✔ Answers:
- J: (2, 4) → J': (4, 8)
- K: (1, 1) → K': (2, 2)
- L: (5, 1) → L': (10, 2)

> You would plot these new points on the graph and connect them to form the dilated triangle.

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5. Graph the dilated image of quadrilateral MNOP using a scale factor of 3 and the origin as the center of dilation.

Again, use the dilation rule: $ (x, y) \rightarrow (3x, 3y) $

#### Step 1: Find original coordinates from the graph:

From the grid:
- M: (3, 4)
- N: (5, 2)
- O: (3, -2)
- P: (0, 1)

#### Step 2: Apply scale factor of 3:

- $ M(3, 4) \rightarrow M'(3 \cdot 3, 3 \cdot 4) = (9, 12) $
- $ N(5, 2) \rightarrow N'(3 \cdot 5, 3 \cdot 2) = (15, 6) $
- $ O(3, -2) \rightarrow O'(3 \cdot 3, 3 \cdot (-2)) = (9, -6) $
- $ P(0, 1) \rightarrow P'(3 \cdot 0, 3 \cdot 1) = (0, 3) $

✔ Answers:
- M: (3, 4) → M': (9, 12)
- N: (5, 2) → N': (15, 6)
- O: (3, -2) → O': (9, -6)
- P: (0, 1) → P': (0, 3)

> Plot these new points and connect them in order to form the dilated quadrilateral.

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✔ Final Answers Summary:

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1. Dilate means to enlarge or shrink a figure.

2. If scale factor < 1, figure gets smaller.

3. If scale factor > 1, figure gets larger.

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4. Triangle JKL dilated by scale factor 2 from (0,0):
- J: (2, 4) → J': (4, 8)
- K: (1, 1) → K': (2, 2)
- L: (5, 1) → L': (10, 2)

5. Quadrilateral MNOP dilated by scale factor 3 from origin:
- M: (3, 4) → M': (9, 12)
- N: (5, 2) → N': (15, 6)
- O: (3, -2) → O': (9, -6)
- P: (0, 1) → P': (0, 3)

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You can now graph these new points on the coordinate planes provided in the worksheet.

Let me know if you'd like help sketching it!