Final answer:
The length of the original segment CD is 5 units. After dilating by a factor of 2 about point C, the length of the dilated image of CD is 10 units.
Step-by-step explanation:
The question involves the concept of dilation in geometry, which is a transformation that produces an image that is the same shape as the original, but is a different size. The segment CD has endpoints at C(0, 3) and D(0, 8). The length of segment CD is the distance between its endpoints, which is the absolute difference between the y-coordinates of points C and D. This can be calculated using the distance formula or simply by subtracting the y-coordinate of C from that of D:
Length of CD = |8 - 3| = 5 units
When segment CD is dilated by a factor of 2 about point C, the length of the segment is also multiplied by the dilation factor. So:
Length of the dilated image of CD = 5 units × 2 = 10 units
Therefore, the length of the dilated image of segment CD is 10 units, which corresponds to option (c) 10.