Rotating a segment 30 degrees around the origin

Question

I got this question wrong on a test, and I would like to know how to solve it!: Segment MN with endpoints M(6,-10) and N(1,0) is rotated 30 degrees about the origin. What are the coordinates of point N after the rotation?-I know it has something to do with making a 30 60 90 triangle, but I don't how to do it.

Answer 1

You had a good hunch with the 30-60-90 triangle. Actually, you have a 30-60-90 triangle that is part of the unit circle! N is a point at the standard starting position of the unit circle. Remember, the unit circle has a radius of 1, and at 0 degrees you would be at (1,0).

 

When you rotate the line segment 30 degrees about the origin, each point gets moved 30 degrees in relation to the origin. You don't need to worry about the rest of the segment or point M.

 

The new N is at (√(3)/2, 1/2)

 

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