Answer:
The correct option is B.
Step-by-step explanation:
It is given that triangle A"B"C" is the image of triangle ABC after transformation.
From the given figure it is noticed that the point C lies on positive y-axis and point C" lies on negative x-axis.
It means the figure is rotated either counterclockwise 90° or clockwise 270°. The rotation rule is
[tex](x,y)\rightarrow (-y,x)[/tex]
The corresponding sides of image A"B"C" are smaller than the preimage ABC.
[tex]k=\frac{A"B"}{AB}=\frac{3}{6}=\frac{1}{2}<0[/tex]
Since k<0, therefore the transformation shows the reduction. The dilation rule is
[tex](x,y)\rightarrow (-\frac{1}{2}y,\frac{1}{2}x)[/tex]
[tex]A(-3,0)\rightarrow (-\frac{1}{2}(0),\frac{1}{2}(-3))\rightarrow (0,-1.5)[/tex]
[tex]B(3,0)\rightarrow (-\frac{1}{2}(0),\frac{1}{2}(3))\rightarrow (0,1.5)[/tex]
[tex]C(0,5.2)\rightarrow (-\frac{1}{2}(5.2),\frac{1}{2}(0))\rightarrow (-2.6,0)[/tex]
Option B is correct.
