3.1. 12 [x1(y2−y3)+x2(y3−y1)+x3(y1−y2)] square units
4. The distance of a point P(x, y) from the origin is ((x)^2+(y)^2)^1/2. The distance between P(x1 ,y1) and Q(x2 , y2 ) is {(x2-x1)^2+(y2-y1)^2}^1/2 The coordinates of the point P(x, y) which divides the line segment joining the points A(x 1 , y 1 ) and B(x 2 , y 2 ) internally in the ratio m1 : m2 are , (m1 x2+ m2 x1)/m1+m2 (m1 y2 m2 y1)/m1+m2 4. The mid-point of the line segment joining the points P(x1 , y1 ) and Q(x2 , y2 ) is (x1+x2)/2,(y1+y2)/2 The area of the triangle formed by the points (x1 , y1 ), (x2 , y2 ) and (x3 , y3 ) is the numerical value of the expression :- 1/2I x1(y1-y3)+x2(y3-y2)+x3(y2-y1)I
