Question

A line segment has endpoints at `(8 ,1 )` and `(7 ,5 )`. If the line segment is rotated about the origin by `pi`, translated horizontally by `- 2`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

(-10 , 1) and (-9 , 5)

Explanation:

Let's begin by naming the endpoints A(8 , 1) and B(7 , 5)

Under a rotation of `pi" about the origin "`
a point ( x , y) → (-x , -y)

step 1 : A (8 , 1 ) → A' (-8 , -1) and B (7 , 5) → B'(-7 , -5)

Under a translation of `((-2),(0)) " point (x , y) → (x-2 , y)"`

step 2 : A'(-8 , -1) → A''(-10 , -1) and B'(-7 ,-5) → B''(-9 , -5)

Under a reflection in the x-axis, a point (x , y) → (x , -y)

step 3 : A'' (-10 , -1) → A'''(-10 , 1) and B''(-9 , -5) → B'''(-9 , 5)

hence new endpoints are (-10 , 1) and (-9 , 5)