Question

A line segment has endpoints at `(6 ,4 )` and `(2 ,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

(-4 ,4) , (0 ,5)

Explanation:

There are 3 steps in this question. So that we can follow the movement of the endpoints let's name them.

A(6 ,4) and B(2 ,5)

Step 1

Under a rotation about O of `pi`

a point (x ,y) → (-x ,-y)

hence A(6 ,4) → A'(-6 ,-4) and B(2 ,5) → B'(-2 ,-5)

Step 2

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

a point (x ,y) → (x+2 ,y)

hence A'(-6 ,-4) → A'' (-4 ,-4) and B'(-2 ,-5) → B''(0 ,-5)

Step 3

Under a reflection in the x-axis

a point (x ,y) → (x ,-y)

hence A''(-4 ,-4) → A'''(-4 ,4) and B''(0 ,-5) → B'''(0 ,5)

`rArr (6 ,4) → (-4 ,4)" and " (2 ,5) → (0 ,5)`