<image> As shown in the figure, △DEF is scaled down to half of its original size. The procedure is as follows: pick any point P, connect DP and take the midpoint A of DP; then connect EP and FP, and take their midpoints B and C respectively to form △ABC. Which of the following statements are correct?
 ① △ABC and △DEF are similar figures by homothety (dilation);
② △ABC and △DEF are similar figures;
③ The ratio of the perimeters of △ABC to △DEF is 1:2;
④ The ratio of the areas of △ABC to △DEF is 1:2.

Choose the correct number of statements:
A. 1 statement____
B. 2 statements____
C. 3 statements____
D. 4 statements