AB=(x,y),故:|AB|=sqrt(x^2+y^2)
AC=(u,v),故:|AC|=sqrt(u^2+v^2)
AB·AC=(x,y)·(u,v)=xu+yv=|AB|*|AC|*cosA
故:cosA=(xu+yv)/(sqrt(x^2+y^2)sqrt(u^2+v^2))
故:sinA=sqrt(1-(xu+yv)^2/(x^2+y^2)(u^2+v^2))
=sqrt((xv-yu)^2/(x^2+y^2)(u^2+v^2))
=|xv-yu|/(sqrt(x^2+y^2)sqrt(u^2+v^2))
=|xv-yu|/(|AB|*|AC|)
故△ABC的面积:S=(1/2)|AB|*|AC|*sinA
=|xv-yu|/2