Question

Find the area of ΔABC whose vertices are A(10, –6), B(2, 5) and C(–1, 3).

Answer 1

A(10,-6), B (2,5) and C(-1,3) are the vertex of  ΔABC. Then,

`(x_1=10,y_1=-6),(x_2=2,y_2=5) and (x_3=-1,y_3=3)`

Area of triangle ABC

`=1/2{x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)}`

`=1/2{10(5-3)+2(3-(-6))+(-1)(-6-5)}`

`=1/2{10(2)+2(9)-1(-11)}`

`=1/2{20+18+11}`

`=1/2(49)`

=24.5 sq. units