Straight Line Question 373

Question: In an isosceles triangle ABC, the coordinates of the points B and C on the base BC are respectively (1, 2) and (2, 1). If the equation of the line AB is $ y=2x $ , then the equation of the line AC is [Roorkee 2000]

Options:

A) $ y=\frac{1}{2}(x-1) $

B) $ y=\frac{x}{2} $

C) $ y=x-1 $

D) $ 2y=x+3 $

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ \angle ABC=\tan \theta =\frac{\frac{1}{2}-1}{1+\frac{1}{2}}=-\frac{1}{3} $ (Here $ m_1=\frac{1}{2},m_2=1) $ $ \because $ $ AB=AC $ ; \ $ \angle ABC=\angle ACB $ Hence $ -\frac{1}{3}=\frac{m-1}{1+m} $
    Þ $ m=\frac{1}{2} $ (Here m is the gradient of line AC) \ Equation of line AC is $ y-1=\frac{1}{2}(x-2) $
    Þ $ y=\frac{x}{2} $ .