Edia | Free math homework in minutes - Free Printable

Let’s solve each problem one by one. We’re dilating shapes about the origin (0,0) using given scale factors. To do this, we multiply each coordinate of every vertex by the scale factor.

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Problem 1: Quadrilateral with scale factor 3

Original vertices (from graph):
- A = (-4, 2)
- B = (-3, -5)
- C = (1, -3)
- D = (4, 3)

Multiply each by 3:
- A’ = (-4×3, 2×3) = (-12, 6)
- B’ = (-3×3, -5×3) = (-9, -15)
- C’ = (1×3, -3×3) = (3, -9)
- D’ = (4×3, 3×3) = (12, 9)

Draw new points and connect them in same order.

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Problem 2: Triangle with scale factor 1/3

Original vertices:
- A = (-9, 3)
- B = (-4, -6)
- C = (4, -6)

Multiply each by 1/3:
- A’ = (-9×1/3, 3×1/3) = (-3, 1)
- B’ = (-4×1/3, -6×1/3) = (-4/3, -2) → approximately (-1.33, -2)
- C’ = (4×1/3, -6×1/3) = (4/3, -2) → approximately (1.33, -2)

Note: Since it's a worksheet, you can leave as fractions or plot approximate decimal positions.

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Problem 3: Quadrilateral with scale factor 1/2

Original vertices:
- A = (-6, 4)
- B = (-6, -6)
- C = (2, 0)
- D = (4, 6)

Multiply each by 1/2:
- A’ = (-6×1/2, 4×1/2) = (-3, 2)
- B’ = (-6×1/2, -6×1/2) = (-3, -3)
- C’ = (2×1/2, 0×1/2) = (1, 0)
- D’ = (4×1/2, 6×1/2) = (2, 3)

Plot these and connect.

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Problem 4: Quadrilateral with scale factor 4

Original vertices:
- A = (-3, 3)
- B = (-2, -3)
- C = (1, 0)
- D = (1, 2)

Multiply each by 4:
- A’ = (-3×4, 3×4) = (-12, 12)
- B’ = (-2×4, -3×4) = (-8, -12)
- C’ = (1×4, 0×4) = (4, 0)
- D’ = (1×4, 2×4) = (4, 8)

Plot and connect.

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Final Answer:

For each problem, the image after dilation is found by multiplying each original vertex coordinate by the scale factor:

1. New vertices: (-12, 6), (-9, -15), (3, -9), (12, 9)
2. New vertices: (-3, 1), (-4/3, -2), (4/3, -2)
3. New vertices: (-3, 2), (-3, -3), (1, 0), (2, 3)
4. New vertices: (-12, 12), (-8, -12), (4, 0), (4, 8)

Draw the new shapes by plotting these points on the respective graphs and connecting them in the same order as the original.