Area of the parallelogram formed by the lines ${{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0$,${{a}_{1}}x+{{b}_{1}}y+{{d}_{1}}=0$and ${{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0$, ${{a}_{2}}x+{{b}_{2}}y+{{d}_{2}}=0$is

Question

Accepted Answer

$\frac{({{d}_{1}}-{{c}_{1}})({{d}_{2}}-{{c}_{2}})}{{{a}_{1}}{{b}_{2}}-{{a}_{2}}{{b}_{1}}}$

Answer

$\frac{({{d}_{1}}-{{c}_{1}})({{d}_{2}}-{{c}_{2}})}{{{[(a_{1}^{2}+b_{1}^{2})(a_{2}^{2}+b_{2}^{2})]}^{1/2}}}$

Answer

$\frac{({{d}_{1}}-{{c}_{1}})({{d}_{2}}-{{c}_{2}})}{{{a}_{1}}{{a}_{2}}-{{b}_{1}}{{b}_{2}}}$

Answer

$\frac{({{d}_{1}}+{{c}_{1}})({{d}_{2}}+{{c}_{2}})}{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}}$

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Question: Area of the parallelogram formed by the lines ${{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0$,${{a}_{1}}x+{{b}_{1}}y+{{d}_{1}}=0$and ${{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0$, ${{a}_{2}}x+{{b}_{2}}y+{{d}_{2}}=0$is

st-line

Question: Area of the parallelogram formed by the lines ${{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0$,${{a}_{1}}x+{{b}_{1}}y+{{d}_{1}}=0$and ${{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0$, ${{a}_{2}}x+{{b}_{2}}y+{{d}_{2}}=0$is

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