A) \[2(a-{a}')x+2(b-{b}')y={{a}^{2}}+{{b}^{2}}-{{{a}'}^{2}}-{{{b}'}^{2}}\]
B) \[(a-{a}')x+(b-{b}')y={{a}^{2}}+{{b}^{2}}-{{{a}'}^{2}}-{{{b}'}^{2}}\]
C) \[2(a-{a}')x+2(b-{b}')y={{{a}'}^{2}}+b{{'}^{2}}-{{a}^{2}}-{{b}^{2}}\]
D) None of these
Correct Answer: A
Solution :
\[m=\frac{-1}{\frac{{b}'-b}{{a}'-a}}=\frac{{a}'-a}{b-{b}'}\]. Midpoint is \[\left( \frac{a+{a}'}{2},\frac{b+{b}'}{2} \right)\] Therefore equation of line is \[y-\left( \frac{b+{b}'}{2} \right)=\frac{{a}'-a}{b-{b}'}\left( x-\frac{a+{a}'}{2} \right)\] \[\Rightarrow 2(b-{b}')y+2(a-{a}')x-{{b}^{2}}+{{{b}'}^{2}}-{{a}^{2}}+{{{a}'}^{2}}=0\].
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