Question

A line segment has endpoints at `(6 ,5 )` and `(5 ,3)`. If the line segment is rotated about the origin by `pi /2`, translated vertically by `2`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

`(6,5)to(-5,-4),(5,3)to(-3,-3)`

Explanation:

Since there are 3 transformations to be performed, label the endpoints A(6 ,5) and B(5 ,3)

First transformation Under a rotation about origin of `pi/2`

`"a point " (x,y)to(-y,x)`

Hence A(6 ,5) → A'(-5 ,6) and B(5 ,3) → B'(-3 ,5)

Second transformation Under a translation `((0),(-2))`

`"a point " (x,y)to(x,y-2)`

Hence A'(-5 ,6) → A''(-5 ,4) and B'(-3 ,5) → B''(-3 ,3)

Third transformation Under a reflection in the x-axis

`"a point " (x,y)to(x,-y)`

Hence A''(-5 ,4) → A'''(-5 ,-4) and B''(-3 ,3) → B'''(-3 ,-3)

Thus after all 3 transformations.

`(6,5)to(-5,-4)" and " (5,3)to(-3,-3)`