Question

The straight line passing through the points $(0,0),(-1,1)$ and $(1,-1)$ has equation:

• A. $2-x=3y$
• B. $y=x$
• C. $2x-y=0$
• D. $x+y=0$

Answer 1

The correct option is D $x+y=0$

We have to check which straight line given in options, passes through the points $(0,0),(-1,1)$ and $(1,-1)$.
Any point lying on the line satisfies its equation.
Let's take option $A,2-x=3y$
For point $(0,0)$, LHS $=2-0=2$, RHS $=3\left(0\right)=0$
LHS $\ne$ RHS
Hence, the line $2-x=3y$ does not passes through $(0,0)$. So, no need to check whether other points lies on the line or not.
Option $B,y=x$
For the point $(0,0)$, $y=x$ holds.
For the point $(-1,1)$, LHS $=1$, RHS $=-1$
LHS $\ne$ RHS
Hence, line does not pass through $(-1,1)$
Option $C,2x-y=0$
For the point $(0,0)$, LHS $=2\left(0\right)-0=0$, RHS $=0$
LHS $=$ RHS.
Now, for $(-1,1)$, LHS $=2(-1)-1=-3\ne$ RHS
Hence, line does not pass through $(-1,1)$.
Option $D,x+y=0$
For point $(0,0)$, LHS $=0+0=0=$ RHS
For point $(-1,1)$, LHS $=-1+1=0=$ RHS
For point $(1,-1)$, LHS $=-1-1=0=$ RHS
Hence, the line $x+y=0$ passes through all the points $(0,0),(-1,1)$ and $(1,-1)$