Let’s solve each dilation problem step by step.
We are given triangles on coordinate grids and asked to dilate them using the given scale factors. Dilation means we multiply each coordinate of the triangle’s vertices by the scale factor, keeping the center of dilation at the origin (0,0) unless otherwise stated — which it isn’t here, so we assume origin.
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Problem 2: dilation of 4
Original triangle vertices (from grid):
Looking at the graph for #2:
- Point A: (-1, 1)
- Point B: (0, 3)
- Point C: (1, 1)
Multiply each by 4:
- A’ = (-1×4, 1×4) = (-4, 4)
- B’ = (0×4, 3×4) = (0, 12)
- C’ = (1×4, 1×4) = (4, 4)
✔ Check: All points scaled correctly from origin.
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Problem 3: dilation of 1/2
Original triangle vertices (graph #3):
- Point A: (2, -2)
- Point B: (4, -2)
- Point C: (5, -4)
Multiply each by 1/2:
- A’ = (2×0.5, -2×0.5) = (1, -1)
- B’ = (4×0.5, -2×0.5) = (2, -1)
- C’ = (5×0.5, -4×0.5) = (2.5, -2)
✔ Check: Fractions handled correctly.
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Problem 4: dilation of 1.5
Original triangle vertices (graph #4):
- Point A: (1, -1)
- Point B: (1, -4)
- Point C: (3, -4)
Multiply each by 1.5 (which is 3/2):
- A’ = (1×1.5, -1×1.5) = (1.5, -1.5)
- B’ = (1×1.5, -4×1.5) = (1.5, -6)
- C’ = (3×1.5, -4×1.5) = (4.5, -6)
✔ Check: Decimal multiplication correct.
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Problem 5: dilation of 1/3
Original triangle vertices (graph #5):
- Point A: (-3, -1)
- Point B: (-1, -3)
- Point C: (-4, -3)
Multiply each by 1/3:
- A’ = (-3×1/3, -1×1/3) = (-1, -1/3)
- B’ = (-1×1/3, -3×1/3) = (-1/3, -1)
- C’ = (-4×1/3, -3×1/3) = (-4/3, -1)
✔ Check: Negative fractions handled correctly.
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Problem 6: dilation of 2
Original triangle vertices (graph #6):
- Point A: (1, -1)
- Point B: (2, -3)
- Point C: (4, -2)
Multiply each by 2:
- A’ = (1×2, -1×2) = (2, -2)
- B’ = (2×2, -3×2) = (4, -6)
- C’ = (4×2, -2×2) = (8, -4)
✔ Check: Simple doubling — looks good.
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Final Answer:
2) Vertices after dilation: (-4, 4), (0, 12), (4, 4)
3) Vertices after dilation: (1, -1), (2, -1), (2.5, -2)
4) Vertices after dilation: (1.5, -1.5), (1.5, -6), (4.5, -6)
5) Vertices after dilation: (-1, -1/3), (-1/3, -1), (-4/3, -1)
6) Vertices after dilation: (2, -2), (4, -6), (8, -4)
Parent Tip: Review the logic above to help your child master the concept of dilation worksheet kuta software.
