|To find the area of triangle whose vertices are given.|
Let A(x1, y1), B(x2, y2) and C(x3, y3) be the vertices of the triangle.
From A,B,C draw the perpendiculars AL, BM and CN on the x axis.
Area of triangle ABC = area of trap ABML + trap ALNC - trap BMNC
= 1/2[MB+LA]ML + 1/2[LA+CN]LN - 1/2[MB+NC]MN
= 1/2(y2+y1) (x1-x2) + 1/2(y1+y3)(x3-x1) - 1/2(y2+y3)(x3-x2)
Example: Find the area of triangle whose vertices are (1,3), (2,4) and (5,6)
Changing the sign, the area of the triangle in magnitude is 1/2.
Directions: Solve the following.