Answer:
[tex]\large\boxed{d=\dfrac{31\sqrt{34}}{34}\approx5.32}[/tex]
Step-by-step explanation:
The formula of a distance between a point (x₀, y₀) and a line Ax + By + C = 0:
[tex]d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}[/tex]
We have the point D(5, 4) and the line 3x + 5y - 4 = 0.
Substitute:
[tex]x_0=5,\ y_0=4,\ A=3,\ B=5,\ C=-4[/tex]
[tex]d=\dfrac{|(3)(5)+(5)(4)-4|}{\sqrt{3^2+5^2}}=\dfrac{|15+20-4|}{\sqrt{9+25}}=\dfrac{|31|}{\sqrt{34}}\cdot\dfrac{\sqrt{34}}{\sqrt{34}}=\dfrac{31\sqrt{34}}{34}[/tex]
