Question

The perpendicular distance of the point P (6,8) from x axis is :

• A. 8
• B. 6
• C. 10
• D. None of these

Hint:

For any point P(x, y):
Perpendicular distance from the {x-axis} is \(|y|\) (the absolute value of the y-coordinate).
Perpendicular distance from the {y-axis} is \(|x|\) (the absolute value of the x-coordinate). Given point P(6,8): Distance from x-axis = y-coordinate = 8. Distance from y-axis = x-coordinate = 6.

Answer 1

The Correct Option is A

Concept: In a 2D Cartesian coordinate system, a point P is represented by an ordered pair \( (x, y) \). 
The \(x\)-coordinate represents the perpendicular distance of the point from the y-axis. 
The \(y\)-coordinate represents the perpendicular distance of the point from the x-axis. Distance is always a non-negative value.

Step 1: Identify the coordinates of the point P The given point is P (6,8). Here, \(x = 6\) and \(y = 8\).

Step 2: Understand "perpendicular distance from the x-axis" The x-axis is the horizontal line where \(y=0\). The perpendicular distance of a point \( (x, y) \) from the x-axis is the length of the vertical line segment from the point down to (or up to) the x-axis. This length is simply the absolute value of the y-coordinate. Imagine plotting the point P(6,8): 
You move 6 units to the right along the x-axis. 
Then, you move 8 units up, parallel to the y-axis. The distance you moved upwards (8 units) is the perpendicular distance from the x-axis.

Step 3: Determine the perpendicular distance For the point P(6,8), the y-coordinate is 8. The perpendicular distance from the x-axis is \(|y| = |8| = 8\) units.

Step 4: Compare with the options The calculated distance is 8. This matches option (1).