# A line segment with endpoints at #(-1 , 2 )# and #(-4, 1 )# is rotated clockwise by #pi #. What are the new endpoints of the line segment?

(-1, 2) ==> (1, -2)

(-4, 1) ==> (4, -1)

Something to note- Rotation by

use the rotation transformation matrix

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Rotating a line segment by (\pi) radians (180 degrees) around the origin results in each point being mirrored to its opposite quadrant, with the same distance from the origin. The coordinates of the points after rotation can be found by negating both the (x) and (y) values of the original points.

The original endpoints are ((-1, 2)) and ((-4, 1)).

After rotation by (\pi) radians:

- The new position of ((-1, 2)) becomes ((1, -2)).
- The new position of ((-4, 1)) becomes ((4, -1)).

Thus, the new endpoints of the line segment after a clockwise rotation by (\pi) are ((1, -2)) and ((4, -1)).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A line segment has endpoints at #(1 ,4 )# and #(7 ,5 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # - 2 #, and reflected about the x-axis, what will the line segment's new endpoints be?
- Point A is at #(8 ,1 )# and point B is at #(2 ,-3 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- Points A and B are at #(2 ,4 )# and #(3 ,5 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #2 #. If point A is now at point B, what are the coordinates of point C?
- Point A is at #(-5 ,-1 )# and point B is at #(2 ,-3 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- Point (w, z) is transformed by the rule (w+5, z) ?

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