A line segment has endpoints at (6 ,5 )(6,5) and (5 ,3)(5,3). If the line segment is rotated about the origin by pi /2 π2, translated vertically by 2 2, and reflected about the x-axis, what will the line segment's new endpoints be?
1 Answer
Dec 11, 2016
Explanation:
Since there are 3 transformations to be performed, label the endpoints A(6 ,5) and B(5 ,3)
First transformation Under a rotation about origin of
pi/2π2
"a point " (x,y)to(-y,x)a point (x,y)→(−y,x) Hence A(6 ,5) → A'(-5 ,6) and B(5 ,3) → B'(-3 ,5)
Second transformation Under a translation
((0),(-2))
"a point " (x,y)to(x,y-2) Hence A'(-5 ,6) → A''(-5 ,4) and B'(-3 ,5) → B''(-3 ,3)
Third transformation Under a reflection in the x-axis
"a point " (x,y)to(x,-y) Hence A''(-5 ,4) → A'''(-5 ,-4) and B''(-3 ,3) → B'''(-3 ,-3)
Thus after all 3 transformations.
(6,5)to(-5,-4)" and " (5,3)to(-3,-3)
