Prove that the area of the parallelogram formed by the lines. a1x+b1y+

1.	Prove that the area of the parallelogram formed by the lines. a1x+b1y+c1=0,a1x+b1y+d1=0,a2x+b2y+c2=0,a2x+b2y+d2=0 is ∣∣(d1−c1)(d2−c2)a1b2−a2b1∣∣ sq. units. Deduce the condition for these lines to form a rhombus.
Answer» Prove that the area of the parallelogram formed by the lines. $a_{1} x + b_{1} y + c_{1} = 0, a_{1} x + b_{1} y + d_{1} = 0, a_{2} x + b_{2} y + c_{2} = 0, a_{2} x + b_{2} y + d_{2} = 0$ is $∣ ∣ \frac{(d_{1} - c_{1}) (d_{2} - c_{2})}{a_{1} b_{2} - a_{2} b_{1}} ∣ ∣$ sq. units. Deduce the condition for these lines to form a rhombus.

Prove that the area of the parallelogram formed by the lines. a1x+b1y+c1=0,a1x+b1y+d1=0,a2x+b2y+c2=0,a2x+b2y+d2=0 is ∣∣(d1−c1)(d2−c2)a1b2−a2b1∣∣ sq. units. Deduce the condition for these lines to form a rhombus.

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Prove that the area of the parallelogram formed by the lines.

$a_{1} x + b_{1} y + c_{1} = 0, a_{1} x + b_{1} y + d_{1} = 0, a_{2} x + b_{2} y + c_{2} = 0, a_{2} x + b_{2} y + d_{2} = 0$ is $∣ ∣ \frac{(d_{1} - c_{1}) (d_{2} - c_{2})}{a_{1} b_{2} - a_{2} b_{1}} ∣ ∣$ sq. units.

Deduce the condition for these lines to form a rhombus.

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Prove that the area of the parallelogram formed by the lines. a1x+b1y+c1=0,a1x+b1y+d1=0,a2x+b2y+c2=0,a2x+b2y+d2=0 is ∣∣(d1−c1)(d2−c2)a1b2−a2b1∣∣ sq. units. Deduce the condition for these lines to form a rhombus.

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