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. So area of triangle formed by these points will be equal to 0.
$\because$ Area of triangle having coordinates $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ is $\frac{1}{2}\times |\left(x_1\right)(y_2-y_3)+\left(x_2\right)(y_3-y_1)+\left(x_3\right)(y_1-y_2)|$
$\therefore \frac{1}{2}\times |x(4+6)+3(-6-y)-5(y-4)|=0\Rightarrow x(4+6)+3(-6-y)-5(y-4)=0\Rightarrow 10x-18-3y-5y+20=0\Rightarrow 10x-8y+2=0\Rightarrow 5x-4y+1=0$
Hence, the point (x,y) lies on the line joining (3, 4) and (-5, -6), if 5x-4y+1=0