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?

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 = ${M}_{3 \times 3}$
$V ' = {M}_{R f} {M}_{T} {M}_{R} V$
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|
|0|