Question

A line segment has endpoints at `(9 ,6 )` and `(5 ,3)`. If the line segment is rotated about the origin by `pi /2`, translated vertically by `2`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

`(9,6)to(6,7) , (5,3)to(3,3)`

Explanation:

Since there are 3 transformations to be performed here, label the points A(9 ,6) and B(5 ,3) so that the change to each point after each transformation can be noted.

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

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

hence A(9 ,6) →A'(6 ,-9) and B(5 ,3) → B'(3 ,-5)

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

`" a point" (x,y)to(x+0,y+2)`

hence A'(6 ,-9) → A''(6 ,-7) and B'(3 ,-5) → B''(3 ,-3)

Third transformation Under a reflection in the x-axis

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

hence A''(6 ,-7) → A'''(6 ,7) and B''(3 ,-3) → B'''(3 ,3)

After all 3 transformations.

`(9,6)to(6,7)" and " (5,3)to(3,3)`