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

The correct option is D

$x+y=0$

Explanation for the correct option:

Option (d):$x+y=0$

Putting the value of $x=a$ and $y=-a$ in the given options

The point $(a,–a)$ only satisfies the equation $x+y=0$

Explanation for the incorrect options:

(a)$x=a$ represent a line which is parallel to $y-axis$ and also it’s ordinate is zero.

(b)$y=a$ represent a line parallel to $x-axis$and it's abscissa is zero.

(c) $y=x$any point in this line will be in the form of $\left(a,a\right)$ as both abscissa and ordinate are equal.

So these can't be the correct option.

Hence, option (d) is the correct answer.