Question

the area of triangle whose vertices are (5,1) ,(1,-1) and (11,4) is

Answer 1

1/2 [ 5      1      1 ]    its called matrices
         1      -1      1
         11    4      1

or 1/ 2[ x1( y2 - y3) + x2 ( y3 - y1) + x3 ( y1 - y2 ) ]

Answer 2

taking (5,1) as a main point
then (1,-1) will change to (-4,-2)
and (1,-1) will change to (6,3)
using vectors ,
A= -4i + (-2)j
B= 6i + 3j
|A×B|/2 = area of triangle
i don't have any paper with me now
but this method is a great one do try
$|a \times b| \div 2$