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

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

Answers (1)

Answer:

(C) On the line y = x

Solution:

First of all we will discuss about x-axis

On x-axis, the value of y is always zero

Therefore point (a, a) cannot lie on x-axis as value of y-coordinate is given as ‘a’.

Now we will discuss about y-axis

On y-axis, the value of x is always zero.

Therefore point of the form (a, a) cannot lie on y-axis as value of x-coordinate is given as ‘a’.

On the line y = x, for each and every value of x there is an equal value of y

For example for x = 1, we get y = 1

Therefore point of the form (a, a) lies on the line y = x.

On the line x + y = 0

Let the value of x is 1

We get y = –1

Hence point of the form (a, a) does not lies on the line x + y = 0.

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

Therefore option (C) is correct.

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