Question

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?

Answer 1

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|
|0|