the area of the triangle formed by the sides. x = 0,x + 2y = 5,3x – y = 1 is
Solution :Given sides are,
x=0
x+2y–5=0
3x–y–1=0
First of all lets recollect the formula for finding the area of the triangle when its sides are given.
△ = 12C1C2C3.∣∣ ∣∣a1b1C1a2b2C2a3b3C3∣∣ ∣∣2
Where C1, C2, C3 are cofactors of the elements c1, c2, c3 respectively. Before doing that lets consider the coefficient matrix.
⎡⎢⎣a1b1C1a2b2C2a3b3C3⎤⎥⎦=⎡⎢⎣10012−53−1−1⎤⎥⎦
C1 = a2b3 – b2a3 = –1 –6 = –7
C2 = b1a3 – a1b3 = 0 – (−1) = 1
C3 = a1b2 – b1a2 = 2
Also
|A| = 1(−2 −5)
=−7
∴ Area
∴ Area =12(−7)1.2.(−7)2
=|−74| = 74sq.Units.