Example Question - scale factor multiplication
Here are examples of questions we've helped users solve.
Dilation of a Point
To perform a dilation on a point with a scale factor centered at the origin, you simply multiply the x and y coordinates of the point by the scale factor. For the point (6, 12) and a scale factor of \( \frac{1}{2} \), the calculation would be as follows: - The x-coordinate after dilation: \( 6 \times \frac{1}{2} = 3 \) - The y-coordinate after dilation: \( 12 \times \frac{1}{2} = 6 \) Therefore, the image of the point (6, 12) after a dilation with a scale factor of \( \frac{1}{2} \) centered at the origin is (3, 6).
Dilation of a Point
To find the image of the point (-8, -4) after a dilation by a scale factor of \( \frac{1}{4} \) centered at the origin, you multiply each coordinate of the original point by the scale factor. So, the new coordinates would be: \( x' = x \cdot \frac{1}{4} = -8 \cdot \frac{1}{4} = -2 \) \( y' = y \cdot \frac{1}{4} = -4 \cdot \frac{1}{4} = -1 \) Therefore, the image of the point (-8, -4) after the dilation is (-2, -1).
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