Find the area of the triangle whose vertices are located at (1,4),(-4,-5),and(2,-3)

Question

Please help me with this problem

Answer 1

There is a formula for the area of a triangle given the co-ordinates of its vertices; it is given by a 3 x 3 determinant (which I cannot easily write)

x₁ y₁ 1

x₂ y₂ 1

x₃ y₃ 1

Multiply the value of this determinant by 1/2

The expansion of this determinant is (1/2)(x₁y₂ + x₂y₃ + x₃y₁ - x₃y₂ - x₂y₁ - x₁y₃) Good luck!

Otherwise you can easily compute the length of the 3 sides and then use Heron's formula, which is

A = sqrt[s(s-a)(s-b)(s-c)] where a, b and c are the sides and s = (1/2)(a + b + c).