Question

The point of the form $(a,-a)$ always lies on the line

• A. $x=a$
• B. $y=a$
• C. $y=x$
• D. $x+y=0$

Answer 1

Answer: (D)

$x+y=0$

For the point of the form $(a,-a)$ to lie on the line, its co ordinates should satisfy the equation,

A) For the line $x=a,$

There is no $y$-coordinate, so it is $0$

Since the point $(a,-a)$ have $y=-a,$ it does not lie on the line.

B) For the line $y=a,$

There is no $x$-value, so $x$ coordinate is $0$

Since the point $(a,-a)$ have $x=a\ne 0,$ it does not lie on the line.

C) For the line $y=x,$

Both $x$ and $y$ co ordinates should be equal

Since, co ordinates of the point $(a,-a)$ are not equal, it does not lie on the line.

D) For the line $x+y=0$

Sum of $x$ and $y$ coordinates should be $0$

Substituting co ordinates of the point $(a,-a)$ in the equation $x+y=0$

We get $a+(-a)=a-a=0$

LHS $=$ RHS

Hence, $(a,-a)$ satisfies $x+y=0$.

Hence, option D is correct.