# A line segment has endpoints at #(3 ,1 )# and #(2 , 0 )#. If the line segment is rotated about the origin by # pi /2 #, translated horizontally by # 1 #, and reflected about the x-axis, what will the line segment's new endpoints be?

##### 1 Answer

Apr 14, 2016

(0 , -3) , (1 , -2)

#### Explanation:

Step 1:

Under a rotation of#pi/2 " about the origin " # a point (x , y) → (-y , x)

Name the points A(3 , 1) and B(2 , 0)

hence A(3 , 1) → A'(-1 , 3) and B → B'(0 , 2)

Step 2:

Under a translation of#((1),(0))# a point (x , y) → (x + 1 , y)

hence A'(-1 , 3) → A''(0 , 3) and B'(0 , 2) → B''(1 , 2)

Step 3:

Under a reflection in the x-axisa point (x , y) → (x , -y)

hence A''(0 , 3) → A'''(0 , -3) and B''(1 , 2) → (1 , -2)