Question

12. Determine the shortest distance from the

point D(5, 4) to the line represented by
3x + 5y - 4 = 0.



I got my distance as the square root of 26890600/12027024
But I’m fairly certain that’s incorrect.

Answer 1

`\large\boxed{d=(31√(34))/(34)\approx5.32}`

Explanation:

The formula of a distance between a point (x₀, y₀) and a line Ax + By + C = 0:

`d=(|Ax_0+By_0+C|)/(√(A^2+B^2))`

We have the point D(5, 4) and the line 3x + 5y - 4 = 0.

Substitute:

`x_0=5,\ y_0=4,\ A=3,\ B=5,\ C=-4`

`d=(|(3)(5)+(5)(4)-4|)/(√(3^2+5^2))=(|15+20-4|)/(√(9+25))=(|31|)/(√(34))\cdot(√(34))/(√(34))=(31√(34))/(34)`