# 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?

Jan 24, 2016

$\left(- 4 , 13\right)$ and $\left(- 5 , 10\right)$

#### Explanation:

In a rotation by $\pi$ (symmetry relatively to the origin O)
$x = - {x}_{0}$ and $y = - {y}_{o}$
The points become
$\left(- 4 , - 9\right)$ and $\left(- 5 , - 6\right)$

A translation vertically by -4 (4 units down relatively to x-axis) means that
$y = {y}_{0} - 4$
The points become
$\left(- 4 , - 13\right)$ and $\left(- 5 , - 10\right)$

In a reflection about the x-axis, $y = 0$ (symmetry relatively to the x-axis)
$y = - {y}_{o}$
The points become
$\left(- 4 , 13\right)$ and $\left(- 5 , 10\right)$