Math worksheet focusing on dilations and translations, featuring problems to graph dilated images of shapes using given scale factors and centers of dilation.

Let’s solve each part step by step.

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Question 1:
In Math, the word *dilate* means to enlarge or shrink a figure.

→ Dilation changes the size of a shape but keeps its shape the same. It can make it bigger (enlarge) or smaller (shrink).

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Question 2:
If a scale factor is less than 1, then your figure gets smaller.

→ Example: Scale factor 0.5 → half the size.

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Question 3:
If a scale factor is greater than 1, then your figure gets larger.

→ Example: Scale factor 2 → twice as big.

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Question 4:
We are given triangle JKL with center of dilation at (0,0) and scale factor = 2.

First, find coordinates of original points from the graph:

Looking at the grid:

- Point J: x=2, y=4 → J(2, 4)
- Point K: x=1, y=1 → K(1, 1)
- Point L: x=4, y=0 → L(4, 0)

To dilate from origin (0,0) with scale factor 2, multiply each coordinate by 2:

- J’ = (2×2, 4×2) = (4, 8)
- K’ = (1×2, 1×2) = (2, 2)
- L’ = (4×2, 0×2) = (8, 0)

✔ Check: All points doubled — correct for scale factor 2 from origin.

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Question 5:
Quadrilateral MNOP, scale factor = 3, center at origin (0,0).

Find original coordinates from graph:

- M: x=1, y=3 → M(1, 3)
- N: x=3, y=2 → N(3, 2)
- O: x=2, y=-2 → O(2, -2)
- P: x=-1, y=0 → P(-1, 0)

Multiply each coordinate by 3:

- M’ = (1×3, 3×3) = (3, 9)
- N’ = (3×3, 2×3) = (9, 6)
- O’ = (2×3, -2×3) = (6, -6)
- P’ = (-1×3, 0×3) = (-3, 0)

✔ Check: All multiplied by 3 — correct.

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Final Answer:

1. enlarge, shrink
2. smaller
3. larger
4.
J: (2, 4) → J’: (4, 8)
K: (1, 1) → K’: (2, 2)
L: (4, 0) → L’: (8, 0)
5.
M: (1, 3) → M’: (3, 9)
N: (3, 2) → N’: (9, 6)
O: (2, -2) → O’: (6, -6)
P: (-1, 0) → P’: (-3, 0)