Consider two parallel lines separated by a distance of 10 units. If one line is translated 5 units to the right, will the lines remain parallel?

Question

Responses
A Yes, the lines will remain parallel.Yes, the lines will remain parallel.
B It depends on the y-intercepts of the lines.It depends on the y-intercepts of the lines.
C It depends on the slopes of the lines.It depends on the slopes of the lines.
D No, the lines will not remain parallel.

Answer 1

The correct response is:

A. Yes, the lines will remain parallel.

When a line is translated horizontally (to the right or left), it does not change its slope; it simply shifts its position. Therefore, the translated line will remain parallel to the original line, even if the distance between them remains unchanged. The slope and parallelism are preserved in this translation.