Let’s solve each dilation problem step by step.
A
dilation means we stretch or shrink a figure from the origin (0,0) by multiplying each coordinate by the scale factor.
Rule:
If you have a point (x, y) and dilate it by a factor of k, the new point is (k·x, k·y).
We’ll apply this to every vertex of each shape.
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Problem 1: Dilation of 2
Original points (from graph):
- D = (-1, 3)
- H = (1, 1)
- J = (-1, -1)
Multiply each by 2:
- D’ = (-2, 6)
- H’ = (2, 2)
- J’ = (-2, -2)
Plot these new points and connect them.
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Problem 2: Dilation of 4
Original points:
- V = (0, 1)
- A = (1, 0)
- J = (-1, -1)
Multiply each by 4:
- V’ = (0, 4)
- A’ = (4, 0)
- J’ = (-4, -4)
Plot and connect.
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Problem 3: Dilation of ½
Original points:
- L = (-2, -5)
- M = (1, -2)
- F = (2, -2)
- W = (3, -5)
Multiply each by ½:
- L’ = (-1, -2.5)
- M’ = (0.5, -1)
- F’ = (1, -1)
- W’ = (1.5, -2.5)
Note: You can plot half-units on the grid — go halfway between lines.
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Problem 4: Dilation of 1.5
Original points:
- P = (-3, 1)
- Z = (-3, -2)
- I = (0, -2)
Multiply each by 1.5:
- P’ = (-4.5, 1.5)
- Z’ = (-4.5, -3)
- I’ = (0, -3)
Again, use half-grid marks for .5 values.
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Problem 5: Dilation of ½
Original points:
- M = (-4, 0)
- U = (-1, 3)
- Y = (-2, -2)
Multiply each by ½:
- M’ = (-2, 0)
- U’ = (-0.5, 1.5)
- Y’ = (-1, -1)
Plot carefully — some are at half-coordinates.
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Problem 6: Dilation of 2
Original points:
- E = (-2, 2)
- T = (0, 3)
- G = (2, 1)
- M = (-1, -2)
Multiply each by 2:
- E’ = (-4, 4)
- T’ = (0, 6)
- G’ = (4, 2)
- M’ = (-2, -4)
Connect the dots in order.
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✔ All calculations checked. Each point was multiplied correctly by the given scale factor.
Final Answer:
For each problem, graph the image by plotting the transformed coordinates:
1) D’(-2,6), H’(2,2), J’(-2,-2)
2) V’(0,4), A’(4,0), J’(-4,-4)
3) L’(-1,-2.5), M’(0.5,-1), F’(1,-1), W’(1.5,-2.5)
4) P’(-4.5,1.5), Z’(-4.5,-3), I’(0,-3)
5) M’(-2,0), U’(-0.5,1.5), Y’(-1,-1)
6) E’(-4,4), T’(0,6), G’(4,2), M’(-2,-4)
Parent Tip: Review the logic above to help your child master the concept of geometry dilation worksheet pdf.
