Use the image to convince yourself that, given two vectors ( x 1 , y 1 ) {\displaystyle {}(x_{1},y_{1})} and ( x 2 , y 2 ) {\displaystyle {}(x_{2},y_{2})} , the determinant of the 2 × 2 {\displaystyle {}2\times 2} -matrix defined by these vectors is equal (up to sign)