Question

A line segment has endpoints at `(5 ,4 )` and `(8 ,7 )`. If the line segment is rotated about the origin by `( pi)/2`, translated vertically by `-2`, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

(4 , 3) and (7 , 6)

Explanation:

Step 1

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

a point (x , y) → (-y , x )

Name the points A(5 , 4) and B(8 , 7)

hence A(5 , 4) → A'(-4 , 5) and B(8 , 7) → B'(-7 , 8)

Step 2

Under a translation of `((0),(-2))`

a point (x , y) → (x , y-2 )

hence A'(-4 , 5) → A''(-4 , 3) and B'(-7 , 8) → B''(-7 , 6)

Step 3

Under a reflection in the y-axis

a point (x , y) → (-x , y)

hence A''(-4 , 3) → A'''(4 , 3) and B''(-7 , 6) → B'''(7 , 6)