A line segment has endpoints at (7 ,6 )(7,6) and (2 ,3 )(2,3). If the line segment is rotated about the origin by pi π, translated horizontally by - 4 −4, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Jun 1, 2016
(7 ,6) → (11 ,-6)
(2 ,3) → (6 ,-3)
Explanation:
There are 3 transformations here. I am naming the points A(7 ,6) and B(2 ,3) so that we can follow what happens to them after each transformation.
1st transformation: under a rotation about origin of
piπ a point (x ,y) → (-x ,-y)
hence A (7 ,6) → A'(-7 ,-6) and B(2 ,3) → B'(-2 ,-3)
2nd transformation : under a translation of
((-4),(0)) a point (x ,y) → (x-4 ,y)
hence A'(-7 ,-6) → A'' (-11 ,-6) and B'(-2 ,-3) → B''(-6 ,-3)
3rd transformation : under a reflection in the y-axis
a point (x ,y) → (-x ,y)
hence A''(-11 ,6) → A'''(11 ,-6) and B''(-6 ,-3) → B'''(6 ,-3)
Thus A(7 ,6) → (11 ,-6) and B(2 ,3) → (6 ,-3)
