Question

A line segment has endpoints at `(3 , 4)` and `(2 , 6)`. If the line segment is rotated about the origin by `(3pi)/2`, translated horizontally by `-2`, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

`(-2,-3)" and "(-4,-2)`

Explanation:

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

`A=(3,4)" and "B=(2,6)`

`color(blue)"First transformation"`

`"under a rotation about the origin of "(3pi)/2`

`• " a point "(x,y)to(y,-x)`

`rArrA(3,4)toA'(4,-3)`

`rArrB(2,6)toB'(6,-2)`

`color(blue)"Second transformation"`

`"under a horizontal translation "((-2),(0))`

`• " a point "(x,y)to(x-2,y)`

`rArrA'(4,-3)toA''(2,-3)`

`rArrB'(6,-2)toB''(4,-2)`

`color(blue)"Third transformation"`

`"under a reflection in the y-axis"`

`• " a point "(x,y)to(-x,y)`

`rArrA''(2,-3)toA'''(-2,-3)`

`rArrB''(4,-2)toB'''(-4,-2)`

`"After all 3 transformations"`

`3,4)to(-2,-3)" and "(2,6)to(-4,-2)`