Question

What was the line that held against the North Korean invasion called

Answer 1

demilitarized zone
The demilitarized zone (DMZ) is a border barrier that divides the Korean Peninsula roughly in half. It was created by agreement between North Korea, China and the United Nations Command in 1953.

Answer 2

38th parallel. 38th parallel, popular name given to latitude 38° N that in East Asia roughly demarcates North Korea and South Korea. The line was chosen by U.S. military planners at the Potsdam Conference (July 1945) near the end of World War II as an army boundary, north of which the U.S.S.R.