Answer:
The value of a is 80
Step-by-step explanation:
The distance of a point
from the y-axis can be written as
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|](https://tex.z-dn.net/?f=d_x%3D%7Cy_0%7C)
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](https://tex.z-dn.net/?f=d_A%3D%7C-30%7C%3D30)
- The distance of point B (5a,2a) from the x-axis can be written as
![d_B=|2a|=2a](https://tex.z-dn.net/?f=d_B%3D%7C2a%7C%3D2a)
Since ![a>0](https://tex.z-dn.net/?f=a%3E0)
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](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7Dd_A%3D%5Cfrac%7B1%7D%7B4%7Dd_B)
Therefore,
![\frac{2}{3}(30)=\frac{1}{4}(2a)](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%2830%29%3D%5Cfrac%7B1%7D%7B4%7D%282a%29)
And solving for a,
![20=\frac{1}{2}a\\a=40](https://tex.z-dn.net/?f=20%3D%5Cfrac%7B1%7D%7B2%7Da%5C%5Ca%3D40)