Mathematics · JEE | DETERMINANTS

The area of the triangle with vertices \( (3, 8) \), \( (-4, 2) \), and \( (5, 1) \) is \( \Delta_1 \). If the vertices are shifted along the line \( y = x \) by 2 units in the positive direction of both axes, the area of the new triangle is \( \Delta_2 \). Then the ratio \( \Delta_1 : \Delta_2 \) is:

1. A
   "2 : 1"
2. B
   "1 : 2"
3. C
   "1 : 1"
4. D
   "1 : 4"