This problem tests understanding of dilation effects on lines with different positions relative to the center. The fundamental rule is that lines passing through the center of dilation map onto themselves, while lines not passing through the center map to parallel lines. With O as the center, line c passes through O, and line d does not pass through O. Therefore, line c maps onto itself (c' = c), and line d maps to a line parallel to d (d' is parallel to d). The correct answer is A. Lines never become perpendicular under dilation, and triangles are similar but not congruent unless the scale factor is 1. A common error is thinking all lines behave the same way, but the key distinction is whether they pass through the center. Always classify lines by their relationship to the center before determining their images.