b) \( \mathrm{A}(5 ; 1), \mathrm{B}(1 ; 3) \) and \( \mathrm{C}(1 ;-2) \) c) \( \mathrm{A}(-2 ;-3), \mathrm{B}(-4 ; 1) \) and \( \mathrm{C}(4 ; 5) \) d) \( \mathrm{A}(0 ; 0), \mathrm{B}(\sqrt{3} ; 1) \) and \( \mathrm{C}(\sqrt{3} ;-1) \) e) \( \mathrm{A}(2 ;-1), \mathrm{B}(-3 ; 4) \) and \( \mathrm{C}(4 ; 5) \) f) \( \mathrm{A}(0 ; 0), \mathrm{B}(p ; q) \) and \( \mathrm{C}(-q ; p) \)

For part b), the triangle formed by points A(5, 1), B(1, 3), and C(1, -2) showcases a fun characteristic: the points A and B are both vertically aligned with point C. This means that the triangle of these points has a unique visual appearance, resembling a right triangle where the base is horizontal and the height is vertical – perfect for learning about right triangles! Moving to part f), when you're dealing with points A(0, 0), B(p, q), and C(-q, p), you have the makings of a very interesting triangle! In fact, this configuration can help illustrate concepts in analytic geometry, particularly how the coordinates transform through symmetry. The result is often a right triangle, depending on the specific values of p and q. It's a great way to dive into deeper discussions of coordinate systems and their properties!