The vertices of a triangle are at points (0, 0), (-1, 1), and (3, 3). What is the area of the triangle?

To find the area of the triangle , we need to use the formula for the area of a triangle , which is : \n \n Area = ( side 1 \ * side 2 ) / 2 \n \n We can use the lengths of the sides of the triangle to find the area . The sides of the triangle are : \n \n Side 1 : ( 0 , 0 ) to (- 1 , 1 ) = x \n Side 2 : (- 1 , 1 ) to ( 3 , 3 ) = y 3 - x \n Side 3 : ( 3 , 3 ) to ( 0 , 0 ) = 3 - 3 x \n \n We can substitute these expressions for x into the formula for the area of the triangle : \n \n Area = ( side 1 \ * side 2 ) / 2 \n = ( x \ * ( 3 - x )) / 2 \n \n To simplify this expression , we can dist ribute the x : \n \n Area = ( x \ * ( 3 - x )) / 2 \n = x \ * ( 3 - x ) / 2 \n \n We can now cancel the x from the numer ator and denomin ator : \n \n Area = ( 3 - x ) / 2 \n \n We can simplify this expression by factor ing out a 2 : \n \n Area = 2 ( 3 - x ) / 2 \n = 3 - 2 x \n \n So the area of the triangle is 3 - 2 x . </s>