Area
of triangle having angular points
(x1,y1) (x2,y2) (x3,y3) is given by the formula
△=12|x1(y2−y3)+x2(y3−y1)+x3(y1−y2)|
△=12∣∣am21(2am2−2am3)+am22(2am3−2am1)+am23(2am1−2am2)∣∣
⇒△=a2∣∣m21(m2−m3)+m22(m3−m1)+m23(m1−m2)∣∣
⇒△=a2∣∣m1m2(m1−m2)−m3(m1+m2)(m1−m2)+m23(m1−m2)∣∣
⇒△=a2∣∣(m1−m2)(m1m2−m3(m1+m2)+m23)∣∣
⇒△=a2|(m1−m2)(m2−m3)(m3−m1)|