Question

c5 = x + 2 y = 1 = − 3 x = − 2 y = 5 =5 = x + 2 y = 1 = − 3 x = − 2 y = 5 =5 = x + 2 y = 1 = − 3 x = − 2 y = 5 =

Answer 1

Answer:

Using ar(Δ)=

2

1

∣x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)∣

ar(ΔABD)=

2

1

∣(−3)(−2+4)+(−1)(−4−4)+x(4−(−2))∣

=

2

1

∣2+6x∣

=∣1+3x∣⟶(i)

ar(ΔACD)=

2

1

∣(−3)(6+4)+5(−4−4)+x(4−6)∣

=

2

1

∣−70−2x∣

=

2

1

∣70+2x∣

=35+x⟶(ii)

∵∣−1∣=1

So,

ar(ΔABD)=2Δ(ACD)

1+3x=70+2x

69=x

∴x=69

Answer 2

Answer:

Using ar(Δ)=

2

1

∣x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)∣

ar(ΔABD)=

2

1

∣(−3)(−2+4)+(−1)(−4−4)+x(4−(−2))∣

=

2

1

∣2+6x∣

=∣1+3x∣⟶(i)

ar(ΔACD)=

2

1

∣(−3)(6+4)+5(−4−4)+x(4−6)∣

=

2

1

∣−70−2x∣

=

2

1

∣70+2x∣

=35+x⟶(ii)

∵∣−1∣=1

So,

ar(ΔABD)=2Δ(ACD)

1+3x=70+2x

69=x

∴x=69

Explanation: