Question

A line segment has endpoints at `(3 ,8 )` and `(4 ,6)`. If the line segment is rotated about the origin by `(pi )/2`, translated vertically by `-6`, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

`(3,8)to(8,-3)" and " (4,6)to(6,-2)`

Explanation:

Since there are 3 transformations to be performed name the endpoints A(3 ,8) and B(4 ,6) so we can 'track' them.

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

a point (x ,y) → (-y ,x)

hence A(3 ,8) → A'(-8 ,3) and B(4 ,6) → B'(-6 ,4)

Second transformation: Under a translation `((0),(-6))`

a point (x ,y) → (x ,y-6)

hence A'(-8 ,3) → A''(-8 ,-3) and B'(-6 ,4) → B''(-6 ,-2)

Third transformation: Under a reflection in the y-axis

a point (x ,y) → (-x ,y)

hence A''(-8 ,-3) → A'''(8 ,-3) and B''(-6 ,-2) → B'''(6 ,-2)

Thus `(3,8)to(8,-3)" and " (4,6)to(6,-2)`