Question

A line 4x + y = 1 passes through the point A(2, -7) meets the line BC whose equation is 3x - 4y + 1 = 0 at the point B. The equation to the line AC so that AB = AC, is

• A. 52x + 89y + 519 = 0
• B. 52x + 89y – 519 = 0
• C. 89x + 52y + 519 = 0
• D. 89x + 52y – 519 = 0

Answer 1

The correct option is A 52x + 89y + 519 = 0


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
Thus the line AC also makes an angle α with BC. If m be the slope of the line AC, then its equation is
y + 7 = m(x - 2) . . . .(ii)
$\Rightarrow m=-4or-\frac{52}{89}$
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