Question

A line segment has endpoints at `(7 ,1 )` and `(7 ,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

`(7,1)to(-9,1),(7,5)to(-9,5)`

Explanation:

Since there are 3 transformations to be performed, label the endpoints A(7 ,1) and B(7 ,5)

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

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

Hence A(7 ,1) → A'(-7 ,-1) and B(7 ,5) → B'(-7 ,-5)

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

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

Hence A'(-7 ,-1) → A''(-9 ,-1) and B'(-7 ,-5) → B''(-9 ,-5)

Third transformation Under a reflection in the x-axis

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

Hence A''(-9 ,-1) → A'''(-9 ,1) and B''(-9 ,-5) → B'''(-9 ,5)

Thus after all 3 transformations.

`(7,1)to(-9,1)" and " (7,5)to(-9,5)`