Question

A line segment has endpoints at `(6 ,5 )` and `(2 ,5 )`. If the line segment is rotated about the origin by `pi`, translated horizontally by `2`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

`(6,5)to(-4,5)" and " (2,5)to(0,5)`

Explanation:

Since there are 3 transformations to be performed, label the endpoints A(6 ,5) and B(2 ,5)

First transformation Under a rotation about the origin of `pi`

`"a point " (x,y)to(-x,-y)`

Hence A(6 ,5) → A'(-6 ,-5) and B(2 ,5) → B'(-2 ,-5)

Second transformation Under a translation `((2),(0))`

`"a point " (x,y)to(x+2,y)`

Hence A'(-6 ,-5) → A''(-4 ,-5) and B'(-2 ,-5) → B''(0,-5)

Third transformation Under a reflection in the x-axis

`"a point " (x,y)to(x,-y)`

Hence A''(-4 ,-5) → A'''(-4 ,5) and B''(0 ,-5) → B'''(0 ,5)

Thus after all 3 transformations.

`(6,5)to(-4,5)" and " (2,5)to(0,5)`