Final answer:
The distance between the points P₁(-6,3) and P₂(1,6) is calculated using the distance formula, derived from the Pythagorean theorem, resulting in √58 units.
Step-by-step explanation:
To find the distance between two points using the distance formula, which is derived from the Pythagorean theorem, we apply the formula:
d(P₁,P₂) = √((x₂ - x₁)² + (y₂ - y₁)²)
Given the points P₁(x₁, y₁) = (-6, 3) and P₂(x₂, y₂) = (1, 6), we substitute the values into the formula.
d(P₁,P₂) = √((1 - (-6))² + (6 - 3)²)
= √((1 + 6)² + (3)²)
= √(7² + 3²)
= √(49 + 9)
= √58
Hence, the distance between the points P₁ and P₂ is √58 units.