Question

Find the distance between the point (3, 5) and a line with the equation 5 x - 3 y + 10 = 0

Answer 1

The distance between the point (3, 5) and a line with the equation 5x – 3y + 10 = 0 will be 10 / √(34) units.

What is the distance between a point and a line?

Let (x₁, y₁) be the point and ax + by + c = 0 be the line.

Then the distance between a point and a line will be

$\rm d = \dfrac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2}}$

The point (3, 5) and a line with the equation 5x – 3y + 10 = 0.

Then the distance between them will be

$\rm d = \dfrac{|5 *3 - 3 *5 + 10|}{\sqrt{5^2 + (-3)^2}}\\d = \dfrac{10 }{\sqrt{34}} \ units$

Learn more about the distance between a point and a line here;

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