A line segment has endpoints at (2 ,5 )(2,5) and (1 , 3 )(1,3). If the line segment is rotated about the origin by pi /2 π2, translated horizontally by 1 1, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Apr 19, 2016
(4 , 2) and (2 , 1)
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(2 , 5) and B(1 , 3)
hence A(2 , 5) →A' (-5 ,2) and B(1 ,3) → B'(-3 , 1)
Step 2 :
Under a translation of
((1),(0)) a point (x , y) → (x +1 , y )
hence A'(-5 , 2) → A''(-4 , 2) and B'(-3 , 1) → B'' (-2 , 1)
Step 3 :
Under a reflection in the y-axis
a point (x , y) → (-x , y)
hence A''(-4 , 2) → A''' (4 , 2) and B''(-2 , 1) → B'''(2 , 1)
