A line segment has endpoints at (3 ,8 )(3,8) and (4 ,6)(4,6). If the line segment is rotated about the origin by (pi )/2 π2, translated vertically by 3 3, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Jan 2, 2017
Explanation:
Since there are 3 transformations to be performed here, label the endpoints A(3 ,8) and B(4 ,6)
First transformation Under a rotation about the origin of
pi/2π2
"a point " (x,y)to(-y,x)a point (x,y)→(−y,x) Hence A(3 ,8)→ A'(-8 ,3) and B(4 ,6) → B'(-6 ,4)
Second transformation Under a translation
((0),(3))
"a point " (x,y)to(x,y+3) Hence A'(-8 ,3) → A''(-8 ,6) and B'(-6 ,4) → B''(-6 ,7)
Third transformation Under a reflection in the y-axis
"a point " (x,y)to(-x,y) Hence A''(-8 ,6) → A'''(8 ,6) and B''(-6 ,7) → B'''(6 ,7)
After all 3 transformations.
(3,8)to(8,6)" and " (4,6)to(6,7)
