A line segment has endpoints at (6 ,4 )(6,4) and (2 ,5 )(2,5). 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
May 18, 2016
(-4 ,4) , (0 ,5)
Explanation:
There are 3 steps in this question. So that we can follow the movement of the endpoints let's name them.
A(6 ,4) and B(2 ,5)
Step 1
Under a rotation about O of
piπ a point (x ,y) → (-x ,-y)
hence A(6 ,4) → A'(-6 ,-4) and B(2 ,5) → B'(-2 ,-5)
Step 2
Under a translation of
((2),(0)) a point (x ,y) → (x+2 ,y)
hence A'(-6 ,-4) → A'' (-4 ,-4) and B'(-2 ,-5) → B''(0 ,-5)
Step 3
Under a reflection in the x-axis
a point (x ,y) → (x ,-y)
hence A''(-4 ,-4) → A'''(-4 ,4) and B''(0 ,-5) → B'''(0 ,5)
rArr (6 ,4) → (-4 ,4)" and " (2 ,5) → (0 ,5)
