The point of the form (a, a) always lies on:(a) On the line x + y = 0(b) On the line y = x(c) x-axis(d) y-axis

The point of the form (a, a) means that the x-coordinate and the y-coordinate are the same.

Let's evaluate each option:

(a) On the line x + y = 0 If we substitute x and y with 'a' in this equation, we get a + a = 0, which simplifies to 2a = 0. This is only true when a = 0. So, the point (a, a) does not always lie on this line.

(b) On the line y = x If we substitute x and y with 'a' in this equation, we get a = a, which is always true. So, the point (a, a) always lies on this line.

(c) x-axis The x-axis is the line where y = 0. Since 'a' is not always 0, the point (a, a) does not always lie on the x-axis.

(d) y-axis The y-axis is the line where x = 0. Since 'a' is not always 0, the point (a, a) does not always lie on the y-axis.

So, the correct answer is (b) On the line y = x.