Question

Find a relation between x and y, if the points $(x,y),(1,2)$ and $(7,0)$ are collinear.

• A. $x+3y-7=0$
• B. $2x+y-6=0$
• C. $x+y-5=0$
• D. None of these

Answer 1

The correct option is A $x+3y-7=0$

Here, $x_1=x,y_1=y,x_2=1,y_2=2,x_3=7,y_3=0$.

Since the given points are collinear, therefore the area of the triangle formed by them must be zero.

$\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]=0$

$\frac{1}{2}\left[x\right(2-0)+1(0-y)+7(y-2\left)\right]=0$

$\frac{1}{2}[2x+6y-14]=0$

$x+3y-7=0$