A dilation stretches or shrinks a figure from a center point — here, always the origin (0, 0). The image is the same shape but a different size (similar, not congruent).
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Multiply both coordinates by the scale factor k.
(x, y) → (kx, ky)
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If k > 1, the figure gets bigger — an enlargement.
k = 2: (3, 1) → (6, 2)
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If 0 < k < 1, the figure gets smaller — a reduction.
k = 1/2: (6, 4) → (3, 2)
Finding the Scale Factor
Divide an image coordinate by the matching preimage coordinate.
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A(2, 4) → A′(6, 12): k = 6 ÷ 2 = 3 — enlargement
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B(4, −2) → B′(2, −1): k = 2 ÷ 4 = 1/2 — reduction
How to Play
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What Is the Rule — Easy: find the scale factor for one point. Medium: match the (x, y) rule for a triangle on the graph. Hard: fraction scale factors from coordinates only.
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Missing Image Point — A triangle and its dilation are graphed, but one image vertex is missing! Use the other points to find the scale factor. Easy & Medium: tap the missing point on the graph. Hard: type the coordinates.
