Final answer:
After a dilation with a scale factor of -3, centered at the origin, the image of the point (4,-5) would fall in Quadrant II because the negative scale factor flips the point to the opposite quadrant and scales it by the absolute value of the factor.
Step-by-step explanation:
The student asked about the result of a dilation transformation with a scale factor of -3 applied to the point (4,-5), centered at the origin. When we dilate a point by a negative scale factor, the image is flipped to the opposite quadrant with respect to the origin and its distance from the origin is multiplied by the absolute value of the scale factor.
Starting with the original point (4, -5) in Quadrant IV, after applying the dilation, the point would move to the opposite quadrant and be scaled up by a factor of 3. Therefore, the image of the point after dilation would be (-4*3, 5*3), which simplifies to (-12, 15). This point falls in Quadrant II, where x is negative and y is positive.