# A line segment has endpoints at (5 ,4 ) and (8 ,7 ). If the line segment is rotated about the origin by ( pi)/2 , translated vertically by -2 , and reflected about the y-axis, what will the line segment's new endpoints be?

Apr 16, 2016

(4 , 3) and (7 , 6)

#### Explanation:

Step 1

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

a point (x , y) → (-y , x )

Name the points A(5 , 4) and B(8 , 7)

hence A(5 , 4) → A'(-4 , 5) and B(8 , 7) → B'(-7 , 8)

Step 2

Under a translation of $\left(\begin{matrix}0 \\ - 2\end{matrix}\right)$

a point (x , y) → (x , y-2 )

hence A'(-4 , 5) → A''(-4 , 3) and B'(-7 , 8) → B''(-7 , 6)

Step 3

Under a reflection in the y-axis

a point (x , y) → (-x , y)

hence A''(-4 , 3) → A'''(4 , 3) and B''(-7 , 6) → B'''(7 , 6)