Question

find the area of a triangle formed by the vertex A(5,2), B(4,7), C(7,-4)

Answer 1

using shifting process
making A as origin we have to add (-5,-2) to A ,B and C

A(5,2). B(4,7). C(7,-4)
add (-5,-2) to A,B and C
you get
A(0,0)
B(-1,5)
C(2,-6)
Area
$\frac{1}{2 } \times |( - 1 \times - 6) - (5 \times 2)| \\ \frac{1}{2} \times 4 = 2$