# A line segment has endpoints at #(6 ,5 )# and #(8 ,7 )#. 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

#color(violet)("After all 3 transformations " color(green)((7, 4)to(-4, -5)" and "(-7, -8)to(-7, 8)#

#### Explanation:

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

#"label the endpoints"#

#A(6,5)" and "B(8,7)#

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

#rArrA(6, 5)toA'(-6, -5)#

#rArrB(8, 7)toB'(-7, -8)#

#color(maroon)"next transformation under a horizontal translation "((2),(0))#

#• " a point "(x,y)to(x + 2, y)#

#rArrA'(-6, -5) to A''(-4, -5)#

#rArrB'(-7, -8) to B''(-5, -8)#

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

#• " a point "(x,y)to(x,-y)#

#rArrA''(-4, -5)toA'''(-4, 5)#

#rArrB''(-7, -8)toB'''(-7, 8)#

#color(violet)("After all 3 transformations " color(green)((7, 4)to(-4, -5)" and "(-7, -8)to(-7, 8)#