Question

A line segment has endpoints at `(4 ,9 )` and `(5 ,6)`. 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

`(-4,13)` and `(-5,10)`

Explanation:

In a rotation by `pi` (symmetry relatively to the origin O)
`x=-x_0` and `y=-y_o`
The points become
`(-4,-9)` and `(-5,-6)`

A translation vertically by -4 (4 units down relatively to x-axis) means that
`y=y_0-4`
The points become
`(-4,-13)` and `(-5,-10)`

In a reflection about the x-axis, `y=0` (symmetry relatively to the x-axis)
`y=-y_o`
The points become
`(-4,13)` and `(-5,10)`