# A line segment has endpoints at #(8 ,1 )# and #(7 ,5 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # - 2 #, and reflected about the x-axis, what will the line segment's new endpoints be?

##### 1 Answer

Apr 12, 2016

(-10 , 1) and (-9 , 5)

#### Explanation:

Let's begin by naming the endpoints A(8 , 1) and B(7 , 5)

Under a rotation of

# pi" about the origin "#

a point ( x , y) → (-x , -y)

step 1 :A (8 , 1 ) → A' (-8 , -1) and B (7 , 5) → B'(-7 , -5)Under a translation of

# ((-2),(0)) " point (x , y) → (x-2 , y)"#

step 2 :A'(-8 , -1) → A''(-10 , -1) and B'(-7 ,-5) → B''(-9 , -5)Under a reflection in the x-axis, a point (x , y) → (x , -y)

step 3 :A'' (-10 , -1) → A'''(-10 , 1) and B''(-9 , -5) → B'''(-9 , 5)hence new endpoints are (-10 , 1) and (-9 , 5)