Distance from (0, 0) to (3, 3)

Calculate the distance between points (0, 0) and (3, 3) using the distance formula.

Answer: Distance = d = 3√2 ≈ 4.242641

Step-by-Step Solution

Step 1 Identify the Points

Point 1: P₁(0, 0)

Point 2: P₂(3, 3)

P₁(0, 0), P₂(3, 3)

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 = 3 - 0 = 3

Δy = y₂ - y₁ = 3 - 0 = 3

Δx = 3, Δy = 3

Step 4 Square the Differences

(Δx)² = (3)² = 9

(Δy)² = (3)² = 9

Sum = 9 + 9 = 18

(Δx)² + (Δy)² = 18

Step 5 Take the Square Root

d = √18

Simplified: d = 3√2

Decimal: d ≈ 4.242641

d = 3√2 ≈ 4.2426

Step 6 Interpretation

This is the distance from the origin

Also represents the magnitude of vector (3, 3)

|(3, 3)| = 4.2426