Step-by-step solution for finding the distance between two points on a coordinate plane.

I need to calculate the distance between two points: (4,6) and (1,2).

Let me work through this step by step using the distance formula.

Step 1: Identify the coordinates
- Point 1: (x₁, y₁) = (4, 6)
- Point 2: (x₂, y₂) = (1, 2)

Step 2: Use the distance formula
The distance formula is: d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Step 3: Calculate the differences
- x₂ - x₁ = 1 - 4 = -3
- y₂ - y₁ = 2 - 6 = -4

Step 4: Square the differences
- (-3)² = 9
- (-4)² = 16

Step 5: Add the squared values
d² = 9 + 16 = 25

Step 6: Take the square root
d = √25 = 5

Let me verify this calculation:
- Distance = √[(1-4)² + (2-6)²]
- Distance = [(-3)² + (-4)²]
- Distance = √[9 + 16]
- Distance = √25
- Distance = 5

This matches what's shown in the work on the page. The calculations are correct.

Final Answer: 5