# A line segment has endpoints at #(4 ,9 )# and #(5 ,2)#. If the line segment is rotated about the origin by #pi #, translated vertically by #-4 #, and reflected about the x-axis, what will the line segment's new endpoints be?

Rotation: (4, 9) ==> (-4, -9) and (5, 2) ==> (-5, -2) it flips to the next quadrant

Translation: (-4, -9) ==> (-4, -5) and (-5, -2) ==> (-5, 2)

Reflection simply flips the y so (x, y) ==> (x, -y)

Reflection (-4, -5) ==> (-4, 5) and (-5, 2) ==> (-5, -2)

You can easily get this by using the:

Rotation, Translation and Reflection Matrices =

Where V is 3D Vector i.e. is the transpose of your vector

|4|

V= |9| |0|

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The new endpoints of the line segment after the described transformations will be:

Endpoint 1: (-9, -4) Endpoint 2: (-2, -11)

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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 #(3 , 2)# and #(1 ,3)#. If the line segment is rotated about the origin by #(3pi)/2 #, translated horizontally by #-5#, and reflected about the x-axis, what will the line segment's new endpoints be?
- A line segment has endpoints at #(9 ,1 )# and #(1 ,2 )#. The line segment is dilated by a factor of #4 # around #(3 ,3 )#. What are the new endpoints and length of the line segment?
- Point A is at #(-5 ,9 )# and point B is at #(-6 ,7 )#. 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?
- A line segment has endpoints at #(3 ,4 )# and #(2 ,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?
- A triangle has corners at #(3, 2 )#, ( 3, 1)#, and #( 4, 3)#. If the triangle is reflected across the x-axis, what will its new centroid be?

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