# A line segment has endpoints at (2 ,5 ) and (1 , 3 ). If the line segment is rotated about the origin by  pi /2 , translated horizontally by  1 , and reflected about the y-axis, what will the line segment's new endpoints be?

Apr 19, 2016

(4 , 2) and (2 , 1)

#### Explanation:

Step 1 :

Under a rotation of $\frac{\pi}{2} \text{ about the origin }$

a point (x , y) → (-y , x)

Name the points A(2 , 5) and B(1 , 3)

hence A(2 , 5) →A' (-5 ,2) and B(1 ,3) → B'(-3 , 1)

Step 2 :

Under a translation of $\left(\begin{matrix}1 \\ 0\end{matrix}\right)$

a point (x , y) → (x +1 , y )

hence A'(-5 , 2) → A''(-4 , 2) and B'(-3 , 1) → B'' (-2 , 1)

Step 3 :

Under a reflection in the y-axis

a point (x , y) → (-x , y)

hence A''(-4 , 2) → A''' (4 , 2) and B''(-2 , 1) → B'''(2 , 1)