A line segment has endpoints at (5 ,4 )(5,4) and (8 ,7 )(8,7). If the line segment is rotated about the origin by ( pi)/2 π2, translated vertically by -2 −2, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Apr 16, 2016
(4 , 3) and (7 , 6)
Explanation:
Step 1
Under a rotation of
pi/2 " about the origin " π2 about the origin a point (x , y) → (-y , x )
Name the points A(5 , 4) and B(8 , 7)
hence A(5 , 4) → A'(-4 , 5) and B(8 , 7) → B'(-7 , 8)
Step 2
Under a translation of
((0),(-2))(0−2) a point (x , y) → (x , y-2 )
hence A'(-4 , 5) → A''(-4 , 3) and B'(-7 , 8) → B''(-7 , 6)
Step 3
Under a reflection in the y-axis
a point (x , y) → (-x , y)
hence A''(-4 , 3) → A'''(4 , 3) and B''(-7 , 6) → B'''(7 , 6)
