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

Answer:

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 = #M_(3xx3)#
#V' = M_(Rf)M_TM_RV#
Where V is 3D Vector i.e. is the transpose of your vector #v = (4, 9, 0); # It means put (4, 9, 0) in vertical form then go for it...
|4|
V= |9| |0|
enter image source here |0|