The distance of the point (2, 3) from the x-axis is:

Question

Accepted Answer

The correct option is 2:
The fundamental concept in coordinate geometry is that the distance of a point $(x, y)$ from the x-axis is given by the absolute value of the y-coordinate, which is $|y|$. In a Cartesian plane, the x-axis is the horizontal line, and the distance from this axis is measured vertically. For the point (2, 3), the x-coordinate is 2 and the y-coordinate is 3. Therefore, the perpendicular distance from the point (2, 3) down to the x-axis is $|3|$, which results in 3 units. This measure indicates how far up the point is located from the horizontal axis.

The incorrect option is 1:
Option 1 suggests the distance is 2. This value corresponds to the x-coordinate of the point (2, 3). The x-coordinate, or the abscissa, measures the horizontal distance of the point from the *y-axis*. It is a common conceptual mistake to interchange the roles of the x and y coordinates when calculating distances to the axes. The x-coordinate (2) is the distance from the vertical y-axis, not the horizontal x-axis.

The incorrect option is 3:
Option 3 suggests the distance is 1. This value is not derived from any component of the point (2, 3) in the context of finding the distance to the x-axis. The distance is defined directly by the y-coordinate (3), making any other arbitrary numerical value incorrect. It does not reflect the vertical separation between the point and the x-axis.

The incorrect option is 4:
Option 4 suggests the distance is 5. This result is typically obtained by incorrectly adding the x and y coordinates ($2 + 3 = 5$). In geometry, coordinates are not added together to find the distance to an axis. Distance calculations are specific, and in this case, the distance to the x-axis is simply the magnitude of the y-coordinate.