Answer:
B. [tex]r_{x-axis}(x,y) \circ R_0,90\degree)[/tex]
Step-by-step explanation:
The vertices of triangle ABC have coordinates A(5,2) B(2,4) and C(2,1).
The mapping for reflection in the x-axis is
[tex](x,y)\to (x,-y)[/tex]
When we reflect triangle ABC in the x-axis, we obtain
A1(5,-2) B1(2,-4) and C1(2,-1).
The mapping for 90 degrees clockwise rotation about the origin is
[tex](x,y)\to (y,-x)[/tex]
When we rotate the resulting triangle through 90 degrees clockwise above the origin, we obtain;
A2(-2,-5) B2(-4,-2) and C2(-1,-2).
The vertices of triangle A''B''C'' also have coordinates A''(-2,-5) B''(-4,-2) and C''(-1,-2).
Hence the rule that describes the composition of transformation that maps ABC to A''B''C'' is
[tex]R_0,90\degree \circ r_{x-axis}(x,y)[/tex]
The correct choice is B.
