A line segment has endpoints at (1 ,5 ) and (0 ,1 ). If the line segment is rotated about the origin by  pi , translated horizontally by  - 4 , and reflected about the y-axis, what will the line segment's new endpoints be?

Nov 27, 2016

$\text{the line segment's new end points are:"A1(5,-5) " and } B 1 \left(4 , - 1\right)$

Explanation:

$\text{first; draw line segment AB like figure above}$

$\text{now rotate the line segment about the origin by } \pi$

$\text{now "A(1,5) rArr " } A ' \left(- 1 , - 5\right)$

$B \left(0 , 1\right) \Rightarrow \text{ } B ' \left(0 , - 1\right)$

$\text{translate horizontally by -4}$

$\text{now "A'(-1,-5) " is } A ' ' \left(- 1 - 4 , - 5\right) = \left(- 5 , - 5\right)$
$B ' \left(0 , - 1\right) \text{ is } B ' ' \left(0 - 4 , - 1\right) = \left(- 4 , - 1\right)$

$\text{finally; reflect the line segment about y-axis}$