Question

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

• A. $x-axis$
• B. $y-axis$
• C. On the line$y=x$
• D. On the line $x+y=0.$

Answer 1

The correct option is C

On the line$y=x$

Explanation for the correct answer:

Option (c): On the line$y=x$

The point of the form $(a,a)$ always lies on the line$y=x$

Since the abscissa and ordinates of the given point are equal ie. $x=y$ so it lie on the line$y=x$.

Explanation for the incorrect options:

(a) the the equation of the line with lies on $x-axis$ is $x=a$,where $a$is any constant.

(b) the the equation of the line with lies on $y-axis$ is $y=a$,where $a$is any constant.

(d) On solving the equation $x+y=0$ we get ,$x=-y$ which does not satisfy the given point.

Therefore, option (C) is the correct answer.