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Jeremiah does not specifically use the term "plumb line" here, but in verse 8, he uses "line," meaning a measuring line: "He has stretched out a line." It is a similar image. When a workman lays down concrete or puts up posts for a fence, he stretches out a line to make sure that his work meets the measurements for that particular project. God has done this as well. He has stretched out a line, and the implication is that, in this case, the daughter of Zion has crossed it! So He said, "That's it!" and He did all these terrible things that Lamentations speaks of. God destroyed the wall, made the people suffer lack and degradation, etc.
In destroying the wall—taking away the people's source of protection—He will determine who trusts Him and who does not. He will see who will stick by Him and His way of life and who will not. When the wall is destroyed, people and their characterss are exposed. Then God will see just where they stand—on which side of the line: on His side or on the other side.
Verse 9 mentions scattering: "Her king and her princes are among the nations." It also speaks of disregard of His law: "The Law is no more." He writes also, "Her prophets find no vision from the LORD," meaning there is a disconnect between God's people and God Himself. They are not getting the instruction they need.
Richard T. Ritenbaugh
The Two Witnesses (Part 5)