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In an isosceles triangle $\mathrm{A B C}$ , the coordinates of the point $\mathrm{B}$ and $\mathrm{C}$ on the base $\mathrm{BC}$ are respectively $\mathrm{(1,2)}$ and $\mathrm{(2,1)}$ . If the equation of the line $\mathrm{A B}$ is $\mathrm{y=2 x}$ , then the equation of the line $\mathrm{ A C}$ is
Option: 1
$y=\frac{1}{2}(x-1)$

Option: 2
$y=\frac{x}{2}$

Option: 3
$y=x-1$

Option: 4
$2 y=x+3$

Answers (1)

best_answer

Slope of B C $=\frac{1-2}{2-1}=-1$

$A B=A C, \, \, \therefore \angle A B C=\angle A C B$

$\Rightarrow\left|\frac{2+1}{1+2(-1)}\right|=\frac{m+1}{1+m(-1)} \Rightarrow \frac{m+1}{1-m}=|-3| \Rightarrow \frac{m+1}{1-m}= \pm 3 \Rightarrow$ $m=2, \frac{1}{2} .$

$\text { But slope of } A B \text { is } 2 ; \quad \therefore \quad m=\frac{1}{2}$ (Here m is the gradient of the line

Equation of the line AC is $y-1=\frac{1}{2}(x-2) \Rightarrow x-2 y=0 \text { or } y=\frac{x}{2}$

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