Final answer:
Option D represents a dilation transformation where each coordinate of the point (8, 4) is multiplied by a scale factor of 1/2 to obtain the point (4, 2).
Step-by-step explanation:
The question is asking to identify which transformation represents a dilation. A dilation is a transformation that scales a figure larger or smaller with respect to a fixed point called the center of dilation. It involves multiplying each coordinate by the same scale factor. Looking at the given options, let's evaluate each transformation:
- A. (8,4)→(−8,4) represents a reflection over the y-axis, not a dilation.
- B. (8,4)→(−4,−8) represents a rotation or reflection, not a dilation.
- C. (8,4)→(11,7) could represent a dilation if both coordinates are multiplied by the same non-zero scale factor. However, to determine if this is indeed a dilation, we would need to divide the new coordinates by the original coordinates. If 11/8 equals 7/4, then this is a dilation with a scale factor of 11/8 or 7/4. Let's check this: 11/8 = 1.375 and 7/4 = 1.75; since these are not equal, this is not a dilation.
- D. ((8, 4) → (4, 2)) represents a dilation since both coordinates are divided by the same factor (8/4 = 2 and 4/2 = 2), which means the points are simply getting closer to the origin by a scale factor of 1/2, making them half as far from the origin as before.
Thus, option D represents a dilation where the scale factor is 1/2.