Question

A line segment has endpoints at `(4 ,0 )` and `(2 ,1 )`. If the line segment is rotated about the origin by `( pi)/2`, translated vertically by `-8`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

`(4,0)to(0,4)" and " (2,1)to(-1,6)`

Explanation:

Since there are 3 transformations to be performed, label the endpoints A(4 ,0) and B(2 ,1)

First transformation Under a rotation about the origin of `pi/2`

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

Hence A(4 ,0) → A'(0 ,4) and B(2 ,1) → B'(-1 ,2)

Second transformation Under a translation `((0),(-8))`

`"a point " (x,y)to(x,y-8)`

Hence A'(0 ,4) → A''(0 ,-4) and B'(-1 ,2) → B''(-1 ,-6)

Third transformation Under a reflection in the x-axis

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

Hence A''(0 ,-4) → A'''(0 ,4) and B''(-1 ,-6) → B'''(-1 ,6)

Thus after all 3 transformations.

`(4,0)to(0,4)" and " (2,1)to(-1,6)`