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

Answer:

The value of a is 80

Step-by-step 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

$\frac{2}{3}d_A=\frac{1}{4}d_B$

Therefore,

$\frac{2}{3}(30)=\frac{1}{4}(2a)$

And solving for a,

$20=\frac{1}{2}a\\a=40$