Question

A line segment has endpoints at `(4 ,7 )` and `(5 ,6)`. If the line segment is rotated about the origin by `pi`, translated vertically by `-2`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

`color(chocolate)("After all 3 transformations " color(gray)((4, 7)to(-4, 9)" and "(5, 6)to(-5, 8)`

Explanation:

`"since there are 3 transformations to be performed"`
`"label the endpoints"`

`A(4, 7)" and "B(5, 6)`

`color(indigo)"transformation of rotation about the origin of "(pi)`

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

`rArrA(4, 7)toA'(-4, -7)`

`rArrB(5, 6)toB'(-5, -6)`

`color(indigo)"next transformation under a vertical translation " ((0),(-2))`

`• " a point "(x,y)to(x, y - 2)`

`rArrA'(-4, -7) to A''(-4, -9)`

`rArrB'(-5, -6) to B''(-5, -8)`

`color(indigo)"last transformation under a reflection in the x -axis"`

`• " a point "(x,y)to(x, -y)`

`rArrA''(-4, -9)toA'''(-4, 9)`

`rArrB''(-5, -8)toB'''(-5, 8)`

`color(chocolate)("After all 3 transformations " color(gray)((4, 7)to(-4, 9)" and "(5, 6)to(-5, 8)`