# A line segment has endpoints at #(9 ,1 )# and #(5 ,3)#. If the line segment is rotated about the origin by #pi #, translated vertically by #-2 #, and reflected about the x-axis, what will the line segment's new endpoints be?

##### 1 Answer

May 29, 2016

(-9 ,3) , (-5 ,5)

#### Explanation:

Since there are 3 transformations to be performed let's begin by naming the endpoints so we can follow what happens to them.

A(9 ,1) and B(5 ,3)(1) Under a rotation about the origin of

#pi# a point (x ,y) → (-x ,-y)

hence A(9 ,1) → A' (-9 ,-1) and B(5 ,3) → B' (-5 ,-3)

(2) Under a translation of

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

hence A'(-9 ,-1) →A'' (-9 ,-3) and B'(-5 ,-3) → B''(-5 ,-5)

(3) Under a reflection in the x-axis.

a point (x ,y) → (x ,-y)

hence A''(-9 ,-3) → A'''(-9 ,3) and B''(-5 ,-5) → B'''(-5 ,5)

hence (9 ,1) → (-9 ,3) and B(5 ,3) → (-5 ,5)