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(a, a), where a > 0, what is the value of a?

Answer 1

The value of a is 80

Step-by-step explanation:

The distance of a point $(x_0,y_0)$ from the y-axis can be written as

$d_y = |x_0|$

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

Similarly, the distance of a point $(x_0,y_0)$ 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 (a,a) from the x-axis can be written as

$d_B = |a| = a$

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,

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

And solving for a,

$20=\frac{1}{4}a\\a=80$

Learn more about distance:

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