Question

The distance of the point A(4a, 3a) from x-axis is :

• A. 3a
• B. -3a
• C. 4a
• D. -4a

Hint:

An easy way to remember this is:
- Distance from \(x\)-axis \(\implies\) Look at the \(y\)-coordinate (take absolute value).
- Distance from \(y\)-axis \(\implies\) Look at the \(x\)-coordinate (take absolute value).
This inverse relationship is a common source of confusion but is very simple to master!

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks us to find the perpendicular distance of a given coordinate point \(A(4a, 3a)\) from the horizontal \(x\)-axis.

Step 2: Key Formula or Approach:
1. In a Cartesian coordinate system, any point \(P\) is represented as \((x, y)\).
2. The coordinate \(x\) represents the perpendicular distance of the point from the \(y\)-axis.
3. The coordinate \(y\) represents the perpendicular distance of the point from the \(x\)-axis.
4. Since distance is always a non-negative scalar quantity, the distance of a point \((x, y)\) from the \(x\)-axis is mathematically defined as the absolute value of its \(y\)-coordinate:
\[ \text{Distance from } x\text{-axis} = |y| \]

Step 3: Detailed Explanation:
1. Identify the coordinates of the given point \(A(4a, 3a)\):
- The \(x\)-coordinate is \(4a\).
- The \(y\)-coordinate is \(3a\).
2. Apply the distance rule:
The perpendicular distance from the \(x\)-axis is the absolute value of the \(y\)-coordinate:
\[ \text{Distance} = |3a| \]
3. In school-level curriculum, coordinate constants (such as \(a\) here) are assumed to be positive unless specified otherwise. Thus:
\[ \text{Distance} = 3a \]
(Note: Even if \(a\) were negative, distance cannot be a negative value, so options (B) and (D) are immediately ruled out).

Step 4: Final Answer:
The distance of the point \(A(4a, 3a)\) from the \(x\)-axis is \(3a\), which corresponds to option (A).