Distance from (1, 2) to (5, 6)

Calculate the distance between points (1, 2) and (5, 6) using the distance formula.

Answer: Distance = d = 4√2 ≈ 5.656854

Step-by-Step Solution

Step 1 Identify the Points

Point 1: P₁(1, 2)

Point 2: P₂(5, 6)

P₁(1, 2), P₂(5, 6)

Step 2 State the Distance Formula

For two points in 2D space:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

This is derived from the Pythagorean theorem

d = √[(x₂-x₁)² + (y₂-y₁)²]

Step 3 Calculate the Differences

Δx = x₂ - x₁ = 5 - 1 = 4

Δy = y₂ - y₁ = 6 - 2 = 4

Δx = 4, Δy = 4

Step 4 Square the Differences

(Δx)² = (4)² = 16

(Δy)² = (4)² = 16

Sum = 16 + 16 = 32

(Δx)² + (Δy)² = 32

Step 5 Take the Square Root

d = √32

Simplified: d = 4√2

Decimal: d ≈ 5.656854

d = 4√2 ≈ 5.6569