Geometry worksheet on dilations with six problems requiring graphing images using specified scale factors.

Since the options ExplainAnswer, TeachTopic, and GeneratePractice are all false, I will only provide the final answers for each problem after working through them step by step.

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Problem 1: Dilation of 2

Original triangle DEF has coordinates:
- D(0, 3)
- E(-1, -1)
- F(1, 0)

Dilate by factor 2 from origin → multiply each coordinate by 2:

- D'(0×2, 3×2) = (0, 6)
- E'(-1×2, -1×2) = (-2, -2)
- F'(1×2, 0×2) = (2, 0)

✔ Final Answer for #1: Triangle with vertices at (0,6), (-2,-2), (2,0)

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Problem 2: Dilation of 4

Original triangle JKL has coordinates:
- J(-1, -1)
- K(0, 1)
- L(1, 0)

Dilate by factor 4:

- J'(-1×4, -1×4) = (-4, -4)
- K'(0×4, 1×4) = (0, 4)
- L'(1×4, 0×4) = (4, 0)

✔ Final Answer for #2: Triangle with vertices at (-4,-4), (0,4), (4,0)

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Problem 3: Dilation of 1/2

Original trapezoid LMFW has coordinates:
- L(2, -4)
- M(3, -2)
- F(4, -2)
- W(5, -4)

Dilate by 1/2:

- L'(2×0.5, -4×0.5) = (1, -2)
- M'(3×0.5, -2×0.5) = (1.5, -1)
- F'(4×0.5, -2×0.5) = (2, -1)
- W'(5×0.5, -4×0.5) = (2.5, -2)

✔ Final Answer for #3: Trapezoid with vertices at (1,-2), (1.5,-1), (2,-1), (2.5,-2)

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Problem 4: Dilation of 1.5

Original triangle PQR has coordinates:
- P(-3, 1)
- Q(-3, -2)
- R(-1, -2)

Dilate by 1.5:

- P'(-3×1.5, 1×1.5) = (-4.5, 1.5)
- Q'(-3×1.5, -2×1.5) = (-4.5, -3)
- R'(-1×1.5, -2×1.5) = (-1.5, -3)

✔ Final Answer for #4: Triangle with vertices at (-4.5,1.5), (-4.5,-3), (-1.5,-3)

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Problem 5: Dilation of 1/2

Original triangle TUV has coordinates:
- T(-3, 2)
- U(-1, 3)
- V(-2, -1)

Dilate by 1/2:

- T'(-3×0.5, 2×0.5) = (-1.5, 1)
- U'(-1×0.5, 3×0.5) = (-0.5, 1.5)
- V'(-2×0.5, -1×0.5) = (-1, -0.5)

✔ Final Answer for #5: Triangle with vertices at (-1.5,1), (-0.5,1.5), (-1,-0.5)

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Problem 6: Dilation of 2

Original triangle EFG has coordinates:
- E(-2, 1)
- F(-1, -2)
- G(1, 0)

Dilate by 2:

- E'(-2×2, 1×2) = (-4, 2)
- F'(-1×2, -2×2) = (-2, -4)
- G'(1×2, 0×2) = (2, 0)

✔ Final Answer for #6: Triangle with vertices at (-4,2), (-2,-4), (2,0)

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Final Answer:
1) (0,6), (-2,-2), (2,0)
2) (-4,-4), (0,4), (4,0)
3) (1,-2), (1.5,-1), (2,-1), (2.5,-2)
4) (-4.5,1.5), (-4.5,-3), (-1.5,-3)
5) (-1.5,1), (-0.5,1.5), (-1,-0.5)
6) (-4,2), (-2,-4), (2,0)