Question - Dilation of a Point by Scale Factor at Origin
Solution:
The question is asking to find the image of the point (12, -4) after a dilation by a scale factor of $$ \frac{1}{3} $$ centered at the origin. Dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The scale factor determines how much larger or smaller the image will be compared to the original figure. When the center of dilation is the origin (0,0), the image of a point can be found by multiplying each coordinate of the point by the scale factor.Given the point (12, -4) and the scale factor of $$ \frac{1}{3} $$, you multiply each coordinate of the point by $$ \frac{1}{3} $$:$$ x' = x \cdot \text{scale factor} = 12 \cdot \frac{1}{3} = 4 $$$$ y' = y \cdot \text{scale factor} = -4 \cdot \frac{1}{3} = -\frac{4}{3} $$Therefore, the image of the point (12, -4) after the dilation is (4, -$$\frac{4}{3}$$).
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