Question

Find the condition that the point P(x, y) may lie on the line joining (3, 4) and (-5, -6).

• A. $5x+4y-1=0$
• B. $5x-4y-1=0$
• C. $5x+4y+1=0$
• D. $5x-4y+1=0$

Answer 1

The correct option is D $5x-4y+1=0$

Since the point P(x,y) lies on the line joining A(3, 4) and B(-5, -6). Therefore, P, A and B are collinear points
$\therefore x(4+6)+3(-6-y)-5(y-4)=0\Rightarrow 10x-18-3y-5y+20=0\Rightarrow 10x-8y+2=0\Rightarrow 5x-4y+1=0$
Hence, the point (x,y) lies on the joining (3, 4) and (-5, -6), if 5x-4y+1=0