Question

A line segment has endpoints at `(2 ,5 )` and `(7 , 3 )`. If the line segment is rotated about the origin by `pi /2`, translated horizontally by `1`, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

`4,2)" and " (2,7)`

Explanation:

Since there are 3 transformations to be performed label the endpoints A(2,5) and B(7,3)

`color(blue)"First transformation"`

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

`• " a point "(x,y)to(-y,x)`

`rArrA(2,5)toA'(-5,2),B(7,3)toB'(-3,7)`

`color(blue)"Second transformation"`

`"under a translation "((1),(0))`

`• " a point "(x,y)to(x+1,y)`

`rArrA'(-5,2)toA''(-4,2)`

`rArrB'(-3,7)toB''(-2,7)`

`color(blue)"Third transformation"`

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

`• " a point "(x,y)to(-x,y)`

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

`rArrB''(-2,7)toB'''(2,7)`

`"hence after all 3 transformations"`

`(2,5)to(4,2)" and " (7,3)to(2,7)`