Let P 1 = ( a 1 , b 1 ) , P 2 = ( a 2 , b 2 ) {\displaystyle {}P_{1}=(a_{1},b_{1}),\,P_{2}=(a_{2},b_{2})} , and P 3 = ( a 3 , b 3 ) {\displaystyle {}P_{3}=(a_{3},b_{3})} be three points in R 2 {\displaystyle {}\mathbb {R} ^{2}} . Express the area of the corresponding triangle by a formula involving a 1 , b 1 , a 2 , b 2 , a 3 , b 3 {\displaystyle {}a_{1},b_{1},a_{2},b_{2},a_{3},b_{3}} .
, and 
be three points in 
. Express the area of the corresponding triangle by a formula involving 
.
