Question

A line segment has endpoints at `(3 ,1 )` and `(2 , 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

(0 , -3) , (1 , -2)

Explanation:

Step 1 :
Under a rotation of `pi/2 " about the origin "`

a point (x , y) → (-y , x)

Name the points A(3 , 1) and B(2 , 0)

hence A(3 , 1) → A'(-1 , 3) and B → B'(0 , 2)

Step 2 :
Under a translation of `((1),(0))`

a point (x , y) → (x + 1 , y)

hence A'(-1 , 3) → A''(0 , 3) and B'(0 , 2) → B''(1 , 2)

Step 3 :
Under a reflection in the x-axis

a point (x , y) → (x , -y)

hence A''(0 , 3) → A'''(0 , -3) and B''(1 , 2) → (1 , -2)