Question

Relation between $x$ and $y$, if the points $(x,y),(1,2)$ and $(7,0)$ are collinear is _____

• A. $x+3y=7$
• B. $x+3y=14$
• C. $-x+3y=7$
• D. $-x+3y=14$

Answer 1

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

For the points $AB=(x,y),BC=(1,2)$ and $CD=(7,0)$ to be collinear they must have area $=0$.

Thus, area of a triangle ABC = $\frac{1}{2}(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))=0$

$=\frac{1}{2}(2x\times 2+6y-14)=0$

$=(2x+6y-14)=0$

Thus, we have the relation $x+3y=7$ for the points to be collinear.