(Should I make a diagram or write an explanation to prove this?)
a) Show that the triangle formed with vertices at (0, 0), (4, 3), and (-2, 11) is a right triangle.
b) Find the area of the triangle.
Find the three lengths of the sides by using the distance formula and then show that these numbers fit in the Pythagorean Theorem.
To find the area, you now know the lengths of the two non-hypotenuse sides of the triangle; one of these will be the height of the triangle, the other will be the base -- use the usual area formula for the area of a triangle.