ANSWER
B. 0.5
EXPLANATION
Triangle ABC has vertices A(5,3), B(3,7), and C(1,4).
After triangle ABC is dilated about the origin, the vertices of the image are
A'(2.5, 1.5), B'(1.5, 3.5), and C'(0.5,2).
Let k be the scale factor of the dilation, then
[tex](x,y)\to (kx,ky)[/tex]
We can then use a point and it's corresponding image to find k.
[tex]A(5,3)\to A'(5k,3k)[/tex]
This implies that
[tex]A'(5k,3k) = A'(2.5,1.5)[/tex]
[tex]5k = 2.5[/tex]
[tex]k = \frac{2.5}{5} [/tex]
[tex]k = \frac{1}{2} = 0.5[/tex]
The scale factor is 0.5
