# 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?

##### 1 Answer

Jan 26, 2016

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)

#### Explanation:

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|

|0|