A line segment with endpoints at $(3, - 2)$ $(3 , -2 )$ and $(5, 8)$ $(5, 8 )$ is rotated clockwise by $\frac{3 π}{2}$ $(3 pi)/2$ . What are the new endpoints of the line segment?

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A line segment with endpoints at $(3, - 2)$ $(3 , -2 )$ and $(5, 8)$ $(5, 8 )$ is rotated clockwise by $\frac{3 π}{2}$ $(3 pi)/2$ . What are the new endpoints of the line segment?

1 Answer

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Answer 1 · 2016-11-20T16:22:58

( 3,-2) would change to (2,3)
and (5,8) would change to (-8,5)

Explanation:

To find the new coordinates, the process of clockwise rotation by $\frac{3 π}{2}$ $(3pi)/2$ can be split in two parts:
I. First rotate by $\frac{π}{2}$ $pi/2$ in which (x,y) $\to$ $->$ (y,-x)

II Next rotate by $π$ $pi$ in which (x,y) $\to$ $->$ (-x,-y)

Thus any point (x,y) on rotation by $\frac{3 π}{2}$ $(3pi)/2$ would become (-y,x)

Thus ( 3,-2) would change to (2,3)
and (5,8) would change to (-8,5)

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A line segment with endpoints at $(3, - 2)$ $(3 , -2 )$ and $(5, 8)$ $(5, 8 )$ is rotated clockwise by $\frac{3 π}{2}$ $(3 pi)/2$ . What are the new endpoints of the line segment?

1 Answer

Explanation:

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1 Answer

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