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: Use the distance formula between a point and its foot on the x-axis, rather than quoting the axis rule directly.
Any point on the $x$-axis has the form $(x, 0)$, since every point on that axis has zero height. The foot of the perpendicular dropped from $A(4a, 3a)$ straight down onto the $x$-axis is the point $M(4a, 0)$, because moving straight down (or up) does not change the $x$-coordinate.

Step 2: Apply the distance formula between $A$ and $M$.
\[ AM = \sqrt{(4a - 4a)^2 + (3a - 0)^2} \]

Step 3: Simplify.
\[ AM = \sqrt{0 + (3a)^2} = \sqrt{(3a)^2} = |3a| \]

Step 4: Decide the sign.
Distance is always taken as a non-negative quantity, and school-level questions like this treat the constant $a$ as positive unless told otherwise. So:
\[ AM = 3a \]
Since a distance can never come out negative, the options $-3a$ and $-4a$ are ruled out immediately, regardless of the sign of $a$.

Step 5: Final Answer.
The distance of point $A(4a, 3a)$ from the $x$-axis is $3a$, so option (A) is correct. \[ \boxed{3a} \]