A line segment has endpoints at (1 ,4 )(1,4) and (3 ,9 )(3,9). If the line segment is rotated about the origin by pi π, translated horizontally by - 2 −2, and reflected about the x-axis, what will the line segment's new endpoints be?
1 Answer
Jul 25, 2016
Explanation:
Since there are 3 transformations to be performed, name the endpoints A(1 ,4) and B(3 ,9) so we can 'track' them.
First transformation Under a rotation about origin of
piπ a point (x ,y) → (-x ,-y)
hence A(1 ,4) → A'(-1 ,-4) and B(3 ,9) → B'(-3 ,-9)
Second transformation Under a translation of
((-2),(0)) a point (x ,y) → (x-2 ,y)
Hence A'(-1 ,-4) → A''(-3 ,-4) and B'(-3 ,-9) → B''(-5 ,-9)
Third transformation Under a reflection in the x-axis
a point (x ,y) → (x ,-y)
hence A''(-3 ,-4) → A'''(-3 ,4) and B''(-5 ,-9) → B'''(-5 ,9)
Thus
(1,4)to(-3,4)" and " (3,9)to(-5,9)
