# A line segment has endpoints at (2 , 3) and (1 , 2). If the line segment is rotated about the origin by (pi)/2 , translated vertically by 3, and reflected about the x-axis, what will the line segment's new endpoints be?

Nov 25, 2016

$\text{the line segment's new endpoints are :M(-3,1) and N (-2,2)}$

#### Explanation:

$\text{1- draw the points given}$

$\text{2-draw a line segment from B to A}$

$\text{3-rotate the line segment about origin by } \frac{\pi}{2}$

$\text{A(2,3),B(1,2) will be " A'(-3,2)" and "B' "(-2,1)}$

$\text{4-now slide the segment 3 unit down}$

$\text{the new coordinates of A is } A ' '$

$A ' ' \left(- 3 , - 1\right)$

$\text{the new coordinates of B is } B ' '$

$B ' ' \left(- 2 , - 2\right)$

$\text{5- now reflect the line segment by x-axis}$

$\text{the reflected line segment is MN and its coordinates are :}$

$\text{M(-3,1) and N(-2,2)}$