Question

Let ABC be a triangle. Let A be the point (1,2) , y = x be the perpendicular bisector AB and x - 2y +1 =0 be the angle bisector of $\angle C$. If the equation of BC is given by ax + by -5 =0, then the value of a + b is

• A. 4
• B. 2
• C. 3
• D. 1

Answer 1

The correct option is B 2

For triangle ABC : A(1,2) and B=(2,1) is the image in y = x.The image of A(1,2) in the ine x-2y+1 =0 is given by
$\frac{x-1}{1}=\frac{y-2}{-2}=\frac{4}{5}$
Hence, coordinates of point are $(\frac{9}{5},\frac{2}{5})$
Since, this point lie on BC, therefore the equation of BC is
3x - y -5 = 0
$\Rightarrow a+b=2$