Question

A line segment has endpoints at `(2 ,5 )` and `(1 , 3 )`. If the line segment is rotated about the origin by `pi /2`, translated horizontally by `1`, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

(4 , 2) and (2 , 1)

Explanation:

Step 1 :

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

a point (x , y) → (-y , x)

Name the points A(2 , 5) and B(1 , 3)

hence A(2 , 5) →A' (-5 ,2) and B(1 ,3) → B'(-3 , 1)

Step 2 :

Under a translation of `((1),(0))`

a point (x , y) → (x +1 , y )

hence A'(-5 , 2) → A''(-4 , 2) and B'(-3 , 1) → B'' (-2 , 1)

Step 3 :

Under a reflection in the y-axis

a point (x , y) → (-x , y)

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