Distance from (0, 0) to (1, 1)

Calculate the distance between points (0, 0) and (1, 1) using the distance formula.

Answer: Distance = d = √2 ≈ 1.414214

Step-by-Step Solution

Step 1 Identify the Points

Point 1: P₁(0, 0)

Point 2: P₂(1, 1)

P₁(0, 0), P₂(1, 1)

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 = 1 - 0 = 1

Δy = y₂ - y₁ = 1 - 0 = 1

Δx = 1, Δy = 1

Step 4 Square the Differences

(Δx)² = (1)² = 1

(Δy)² = (1)² = 1

Sum = 1 + 1 = 2

(Δx)² + (Δy)² = 2

Step 5 Take the Square Root

d = √2

Cannot simplify further

Decimal: d ≈ 1.414214

d = √2 ≈ 1.4142

Step 6 Interpretation

This is the distance from the origin

Also represents the magnitude of vector (1, 1)

|(1, 1)| = 1.4142