Question

What is the area of triangle QRS? Q(-1 , 2) R(1 , -4) S(-2 , -2)

Answer 1

$\left[\begin{array}{ccc}-1&2&1\\1&-4&1\\-2&-2&1\end{array}\right]$

Find the determinant

D = [(-1).(-4).1 + 2.1.(-2) + 1.1.(-2)] - [1.(-4).(-2) + (-1).1.(-2) + 2.1.1]

D = [4 - 4 - 2] - [8 + 2 + 2]

D = -10 - 12

D = -22

A = |D|/2

A = |-22|/2

A = 22/2

A = 11