If the distance of the point (4,a) from x -axis is half its distance from y-axis, then find a.

Given that distance of (4,a) from x-axis is half the distance from y-axis.
The distance between two points (

x_{1}, y_{1}

) and (

x_{2}, y_{2}

) is given by,

\sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}

.
The distance between the point

(4, a)

and

x - axis

can be determined by assuming a point

(4, 0)

x - axis

.
Therefore, the distance between

(4, a)

and

(4, 0)

= \sqrt{(4 - 4)^{2} + (0 - a)^{2}}

\Rightarrow a

Also, the distance between the point

(4, a)

and

y - axis

can be determined by assuming a point

(0, a)

y - axis

.
Therefore, the distance between

(4, a)

and

(0, a)

= \sqrt{(0 - 4)^{2} + (a - a)^{2}}

\Rightarrow 4

According the given condition,

\Rightarrow a = \frac{1}{2} \times 4

\Rightarrow a = 2

So, the value of a is

2

.
Hence, option 2 is correct.

If the distance of the point $(4, a)$ from $x - axis$ is half its distance from $y - axis$ , then find a.