Question

Choose the correct alternative answer for the following question.

Any point on the line $y=x$ is of the form of:

• A. $(b,b)$
• B. $(0,b)$
• C. $(b,0)$
• D. None of these

Answer 1

The correct option is A

$(b,b)$

Step-1: Explanation for the correct option:

Option (A): Given equation of the line is $y=x$

Substitute the point $(b,b)$ in the given equation $y=x$

$\Rightarrow$ $b=b$

$\Rightarrow$L.H.S.$=$ R.H.S.

$\Rightarrow$The point $(b,b)$ satisfies the given equation

Thus option (A) is correct

Step-2: Explanation for the incorrect options

Option (B): Given equation of the line is $y=x$

Substitute the point $(0,b)$ in the given equation $y=x$

$\Rightarrow$ $b\ne 0$

$\Rightarrow$L.H.S.$\ne$ R.H.S.

$\Rightarrow$The point $(0,b)$ does not satisfy the given equation

Thus option (B) is incorrect

Option (C): Given equation of the line is $y=x$

Substitute the point $(b,0)$ in the given equation $y=x$

$\Rightarrow$ $0\ne b$

$\Rightarrow$L.H.S.$\ne$ R.H.S.

$\Rightarrow$The point $(b,0)$ does not satisfy the given equation

Thus option (C) is incorrect

Hence, the correct option is option (A)