Question

Point P lies on line k. A dilation of line k is performed with center P and scale factor 5. Which best describes the resulting line m?

A. Line m and line k are identical.
B. Line m and line k are perpendicular.
C. Line m and line k are parallel.
D. Line m and line k are intersecting but not perpendicular.

Answer 1

A dilation with the center on the line itself will produce a line that is parallel to the original line; hence, line m and line k are parallel.

Step-by-step explanation:

When a dilation is performed on a line with the center of dilation lying on the line and a scale factor is applied, the resulting line is always parallel to the original line. Since point P lies on line k and dilation is performed with center P and a scale factor of 5, line m will be a version of line k that has been scaled up by a factor of 5. However, this scaling does not affect the direction or orientation of the line. Therefore, the correct answer is: C. Line m and line k are parallel.