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A polygon will be dilated on a coordinate grid to create a larger polygon. The polygon is dilated using the origin as the center of dilation.
Which rule could represent this dilation?
A. (x, y) → ( (4/5)x, (4/5)y)
(x, y) → ( (3/2)x, (3/2)y)
(x, y) → (x + 5, y + 5)
(x, y) → (x + 5/4, y + 5/4)
The correct rule that represents a dilation of a polygon using the origin as the center of dilation is:
(x, y) → ( (3/2)x, (3/2)y).
Explanation:
In dilation, the coordinates of each point are multiplied by a scale factor. The rule (x, y) → ( (3/2)x, (3/2)y) indicates a scale factor of 3/2, which means the polygon will increase in size by 1.5 times (or 150%) its original dimensions. A scale factor greater than 1 results in a larger polygon, while the other options either represent a smaller dilation or a translation (movement) of the polygon rather than a dilation.