Question

The points A(1,4) B(-2,1) C(4,1) forms a triangle finds its area please give the explanation step by step​

Answer 1

Answer

A(1,2),B(−5,1),C(1,4)

AB=

(−5−1)

2

+(1−(−2))

2

=

45

BC=

(1−(−5))

2

+(4−1)

2

=

45

∵AB=BC

Hence it is isoceles Δ

CA=

(1−1)

2

+(4−(−2))

2

=

6

2

=6

Answer 2

Step-by-step explanation:

let

A(X1, Y1) = A(1,4)

B(X2, Y2) = B(-2,1)

c(X3,Y3) = c(4,1)

area of triangle =

½ [ X1 (Y2-Y3) + X2(Y3-Y1) + X3(Y1-Y2) ]

substituting values of A,B,C in formula

area of triangle ABC

= ½ [ 1(1-1) + -2(1-4) + 4(4-1) ]

= ½ [ 0 + 6 +12]

= ½ × 18

= 9