Final answer:
When rectangle QRST is dilated by a scale factor of 3 through the origin, the coordinates of point Q are tripled. Evaluating the given options, the correct coordinates for point Q after the dilation are (-3, -21).
Step-by-step explanation:
If rectangle QRST is dilated by a scale factor of 3 through the origin, the coordinates of each point will be multiplied by 3. Therefore, if we assume that point Q had original coordinates (x, y), after dilation, Q's coordinates will be (3x, 3y).
Let's examine the options provided:
- A. (1,21) would not be correct since if Q's original coordinates were (1/3, 7), they are not very likely for a rectangle that is positioned at the origin.
- B. (-3, -21) seems plausible if Q's original coordinates were (-1, -7), which, after dilation by a factor of 3, would result in (-3, -21).
- C. (3, 21) could be correct if Q's original coordinates were (1, 7).
- D. (3, 7) is incorrect because if these were the coordinates post-dilation, the pre-dilation coordinates would be (1, 7/3), which do not seem suitable for an original position of a rectangle at the origin.
So the correct answer is B. (-3,-21), assuming that the rectangle QRST was originally centered at the origin.