In abc, ab = x, bc = y, and ca = 2x. a similarity transformation with a scale factor of 0.5 maps abc to mno, such that vertices m, n, and o correspond to a, b, and c, respectively. if om = 5, what is ab?

we have 
AB = xwith a scale factor of 0.5= x*0.5=0.5x
BC = ywith a scale factor of 0.5= y*0.5=0.5y
CA = 2xwith a scale factor of 0.5= 2x*0.5=x

AB with a scale factor = MN
BC with a scale factor =  NO
AC with a scale factor = OM

 MN=0.5x

NO=0.5y

OM=AC=x=5

X=5
AB=x=5

The answer is AB=5