Final answer:
The equation of the perpendicular bisector of line CD will have a slope that is the negative reciprocal of CD's slope. Without the specific coordinates of points C and D, it's not possible to determine the exact equation from the options provided, but it will be one with a slope of -1/7, which are options C and D.
Step-by-step explanation:
The perpendicular bisector of line segment CD will be a line that is perpendicular to CD and cuts it into two equal lengths.
To find the equation of the perpendicular bisector, you need to know the slope of line CD. The slope of the perpendicular bisector will be the negative reciprocal of CD's slope. If the slope of CD, for example, was 7 (from option A), then the slope of the perpendicular bisector would be -1/7. This is because the product of the slopes of two perpendicular lines in the plane is -1.
Therefore, the correct answer from the given options must have a slope of -1/7. Next, you need to determine the correct y-intercept for the bisector, which depends on the specific coordinates of points C and D. In this case, without those specific coordinates or additional context, we would look for the option with a slope of -1/7, which are options C and D. The correct y-intercept cannot be determined without additional information.