Parallel lines m and n are cut by another line t. what is the locus of points equidistant from lines m and n and 2 cm from the transversal

Question

dumbcow · Answer

every point is 2 cm away from line t ?

directrix · Answer

In 2-space, the locus will be 4 points, I think. I'll draw the picture.

dumbcow · Answer

seems like the locus would consist of only 2 points ...

dumbcow · Answer

or 4 maybe, but im not seeing it

directrix · Answer

Two is correct.
Explanation follows.

directrix · Answer

The red line is the locus of points equidistant from the given parallel lines m and n. The two The two blue lines are the locus of points in the plane at distance 2 from the given line t in the plane. The points that are equidistant from the given parallel lines AND also at distance 2 from line t are the two points A and B formed by the intersection of the red and blue locus lines.