Given:
A quadrilateral QRST.
To find:
The coordinates of Q' after the transformation of [tex](T_{<-1,2>}\circ R_{x-axis})(QRST)[/tex].
Solution:
From the given figure, it is clear that
[tex]Q=(1,3)[/tex]
[tex](T_{<-1,2>}\circ R_{x-axis})(QRST)[/tex] means the figure QRST first reflected across the x-axis, then translated by [tex]T_{<-1,2>}[/tex].
Figure QRST reflected across the x-axis, then
[tex](x,y)\to (x,-y)[/tex]
[tex]Q(1,3)\to Q_1(1,-3)[/tex]
After that, it is translated by [tex]T_{<-1,2>}[/tex].
[tex](x,y)\to (x-1,y+2)[/tex]
[tex]Q_1(1,-3)\to Q'(1-1,-3+2)[/tex]
[tex]Q_1(1,-3)\to Q'(0,-1)[/tex]
Therefore, the coordinates of Q' are (0,-1).
Note: All options are incorrect.
