Question

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

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The value of a is 2

Step-by-step explanation:

We know,

Distance is given as :

$\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }$

Finding the distance of the point ( 4 , a ) from x-axis :

The perpendicular from point ( 4 , a ) on x - axis will fall on ( 4 , 0 )

Substituting the values in the distance formula ,

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

= √a²

= a

So,

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

Similarly,

Finding the distance of the point ( 4 , a ) from y-axis :

The perpendicular from point ( 4 , a ) on y - axis will fall on ( 0 , a )

Substituting the values in the distance formula ,

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

= √4²

= 4

So,

The distance of the point ( 4 , a ) from y-axis is 4

According to question,

The distance of the point ( 4, a ) from x-axis is half the distance from y-axis, that is ,

$a=\frac{1}{2} *4$

a = 2

Hence,

The value of a is 2