Calculate the distance from the point (3,5) to the line y = x + 4.

Question

geometry question caculating distance

Answer 1

The point = (3, 5) and line : y = x + 4 ⇒ x - y + 4 = 0.

Calculate the distance form the point (x₁, y₁) to the line ax + by + c = 0 by using formula :

d = (ax₁ + by₁ + c)/√(a² + b²)

d = [(1)(3) + (-1)(5) + 4]/√[(1)² + (-1)²]

d = (3 - 5 + 4)/√(1 + 1)

d = 2/√2

d = √2 units.