Answer:
The value of a is 80
Step-by-step explanation:
The distance of a point [tex](x_o,y_0)[/tex] from the y-axis can be written as [tex]d_y=|x_o|[/tex] because the x-coordinate of the y-axis is zero.
Similarly, the distance of a point from the x-axis can be written as [tex]d_x=|y_0|[/tex]
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
[tex]d_A=|-30|=30[/tex]
- The distance of point B (5a,2a) from the x-axis can be written as
[tex]d_B=|2a|=2a[/tex]
Since [tex]a>0[/tex]
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
[tex]\frac{2}{3}d_A=\frac{1}{4}d_B[/tex]
Therefore,
[tex]\frac{2}{3}(30)=\frac{1}{4}(2a)[/tex]
And solving for a,
[tex]20=\frac{1}{2}a\\a=40[/tex]
