Final answer:
The correct answer is option c, which states the rule for dilation as (x, y) becomes (1/4x, 1/4y). This reflects a reduction in size by a factor of four for both the x and y coordinates when dilated from the origin.
Step-by-step explanation:
The coordinate rule for a dilation centered at the origin with a scale factor of 1/4 is option c. The new coordinates will be a quarter of the original coordinates. If a point has coordinates (x, y), after dilation with a scale factor of 1/4, the new coordinates will be (1/4x, 1/4y). This scales down both the x and y values by a factor of 4, making the image four times smaller than the original. The scale factor works identically on all points because the dilation is centered at the origin, where multiplying by a fraction smaller than 1 reduces the magnitude of the coordinates, thus bringing them closer to the origin.
For example, if the scale dimension is 4, then you can figure out the actual dimension using the proportion 1:2 = 4:x. Similarly, given a scale factor of 1/4 and a scale measurement of 8 inches, the actual size can be calculated by setting up a proportion such as 1/4 inch to 4 feet equals 8 inches to x feet.