Question

If 2/3 of the distance from the y-axis to point A (−30, −45) is equal to 1/4 of the distance from the x-axis to point B(5a, 2a), where a > 0, what is the value of a?

Answer 1

The value of a is 80

Explanation:

The distance of a point
`(x_o,y_0)` from the y-axis can be written as
`d_y=|x_o|` because the x-coordinate of the y-axis is zero.

Similarly, the distance of a point from the x-axis can be written as
`d_x=|y_0|`

since the y-coordinate of the x-axis is zero.

In this problem:

- The distance of the point A (−30, −45) from the y-axis can be written as

`d_A=|-30|=30`

- The distance of point B (5a,2a) from the x-axis can be written as

`d_B=|2a|=2a`

Since
`a>0`

We are told that 2/3 of the distance from the y-axis to point A (−30, −45) is equal to 1/4 of the distance from the x-axis to point B(a, a), which means

`(2)/(3)d_A=(1)/(4)d_B`

Therefore,

`(2)/(3)(30)=(1)/(4)(2a)`

And solving for a,

`20=(1)/(2)a\\a=40`