After a rotation of 180° counterclockwise around the origin, the points L, M and N will change to L' = (5, - 10), M' = (0, 10) and N' = (9, 6).
When rotating a point 180 degrees counterclockwise about the origin, the point changes from point A(x, y) and becomes A' (- x, - y) that is both the x and y coordinate becomes negative.
Now, we have the points:
L = (- 5, 10)
M = (0, - 10)
N = (- 9, - 6)
After rotating it 180 degrees counterclockwise about the origin, we will get the points as:
L' = (5, - 10)
M' = (0, 10)
N' = (9, 6)
Therefore, after a rotation of 180° counterclockwise around the origin, the points L, M and N will change to L' = (5, - 10), M' = (0, 10) and N' = (9, 6).
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