# What is the distance between F and the line segment DC?

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A square ABCD has a side length 10 and E is the midpoint of AD. Fold the square from the vertex A along line segment BE, such that A moves to the point F, as shown:

What is the distance between F and the line segment DC?

posted Jul 22, 2020
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Starting from his home, Kay moves 40km towards North. He then takes a right turn and walks 30 km to reach point D. From there, he turns towards North-West and moves 50 km. After which he moved 40 km towards North and reaches a point which is in line with his home and the point where he took the first turn. Then, he turns and travels towards South-West for 80√2 km to reach point F which is inline with point D and the point where he took the first turn. From F, he finally turned 135 degrees towards his right and walked 80 km to reach point E.

Q: In which direction is point E with respect to the point D and what is the shortest distance between point F and point D?