A) \[52x+89y+519=0\]
B) \[\beta \]
C) \[89x+52y+519=0\]
D) \[89x+52y-519=0\]
Correct Answer: A
Solution :
Slopes of \[AB\] and BC are ? 4 and \[\frac{3}{4}\] respectively. If \[\alpha \] be the angle between \[AB\] and \[BC\], then \[\tan \alpha =\frac{-4-\frac{3}{4}}{1-4\left( \frac{3}{4} \right)}=\frac{19}{8}\] .....(i) Since \[AB=AC\] \[\Rightarrow \angle ABC=\angle ACB=\alpha \] Thus the line AC also makes an angle \[\alpha \]with BC. If m be the slope of the line AC, then its equation is \[y+7=m(x-2)\] .....(ii) Now \[\tan \alpha =\pm \left[ \frac{m-\frac{3}{4}}{1+m.\frac{3}{4}} \right]\Rightarrow \frac{19}{8}=\pm \frac{4m-3}{4+3m}\] Þ \[m=-4\]or ?\[\frac{52}{89}\]. But slope of AB is ? 4, so slope of AC is \[-\frac{52}{89}\]. Therefore the equation of line AC given by (ii) is \[52x+89y+519=0\].You need to login to perform this action.
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