# A line segment has endpoints at #(4 ,7 )# and #(5 ,6)#. 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

#color(chocolate)("After all 3 transformations " color(gray)((4, 7)to(-4, 9)" and "(5, 6)to(-5, 8)#

#### Explanation:

#"since there are 3 transformations to be performed"#

#"label the endpoints"#

#A(4, 7)" and "B(5, 6)#

#color(indigo)"transformation of rotation about the origin of "(pi) #

#rArrA(4, 7)toA'(-4, -7)#

#rArrB(5, 6)toB'(-5, -6)#

#color(indigo)"next transformation under a vertical translation " ((0),(-2))#

#• " a point "(x,y)to(x, y - 2)#

#rArrA'(-4, -7) to A''(-4, -9)#

#rArrB'(-5, -6) to B''(-5, -8)#

#color(indigo)"last transformation under a reflection in the x -axis"#

#• " a point "(x,y)to(x, -y)#

#rArrA''(-4, -9)toA'''(-4, 9)#

#rArrB''(-5, -8)toB'''(-5, 8)#

#color(chocolate)("After all 3 transformations " color(gray)((4, 7)to(-4, 9)" and "(5, 6)to(-5, 8)#