Question

A line segment has endpoints at `(3 ,1 )` and `(0 , 0 )`. If the line segment is rotated about the origin by `pi /2`, translated horizontally by `1`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

(3 ,1) → (0 ,-3) and (0 ,0) → (1 ,0)

Explanation:

Since there are 3 transformations to be performed, name the endpoints A(3 ,1) and B(0 ,0) so that we can 'track' them.

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

a point (x ,y) → (-y ,x)

hence A(3 ,1) →A' (-1 ,3) and B(0 ,0) → B'(0 ,0)

Second transformation Under a translation `((1),(0))`

a point (x ,y) → (x+1 ,y)

hence A'(-1 ,3) → A''(0 ,3) and B'(0 ,0) → B''(1 ,0)

Third transformation Under a feflection in the x-axis

a point (x ,y) → (x ,-y)

hence A''(0 ,3) → A'''(0 ,-3) and B''(1 ,0) → B'''(1 ,0)

Thus (3 ,1) → (0 ,-3) and (0 ,0) → (1 ,0)