Answer :
The value of a is 80
Step-by-step explanation:
The distance of a point [tex](x_0,y_0)[/tex] from the y-axis can be written as
[tex]d_y = |x_0|[/tex]
because the x-coordinate of the y-axis is zero.
Similarly, the distance of a point [tex](x_0,y_0)[/tex] 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 (a,a) from the x-axis can be written as
[tex]d_B = |a| = a[/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}a[/tex]
And solving for a,
[tex]20=\frac{1}{4}a\\a=80[/tex]
Learn more about distance:
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