Question

23. The graph of 2x = 1 is parallel to the (a) x-axis at a distance of 1 unit (C) x-axis at a distance of 1/2 unit (b) y-axis at a distance of 1 unit (d) y-axis at a distance of unit 1/2 unit​

Answer 1

The graph 2x = 1 is parallel to the y-axis at a distance of 1/2 unit. Option D is the correct answer.

The given question can be solved by using the concepts of coordinate geometry.

• Consider a point (x, y) in the 2D coordinate system. The point P(x, y) is at a distance of y units from the x-axis and at a distance of x units from the y-axis.
• The line y = k is always parallel to the x-axis with a distance of k units. Similarly the link x = d is always parallel to the y-axis with a distance of d units.
• The graph of the line 2x = 1 will be a straight line parallel to the y-axis.

The given line is 2x = 1, The given line can be transformed as,

=> 2x = 1,

=> x = 1/2 unit.

From the mentioned properties above, the line x = 1/2 is parallel to the y-axis at a distance of 1/2 unit.

Therefore, the line 2x = 1 is parallel to the y -axis at a distance of 1/2 unit. Hence, Option D is the correct answer.