Distance from (0, 0) to (2, 4)

Calculate the distance between points (0, 0) and (2, 4) using the distance formula.

Answer: Distance = d = 2√5 ≈ 4.472136

Step-by-Step Solution

Step 1 Identify the Points

Point 1: P₁(0, 0)

Point 2: P₂(2, 4)

P₁(0, 0), P₂(2, 4)

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 = 2 - 0 = 2

Δy = y₂ - y₁ = 4 - 0 = 4

Δx = 2, Δy = 4

Step 4 Square the Differences

(Δx)² = (2)² = 4

(Δy)² = (4)² = 16

Sum = 4 + 16 = 20

(Δx)² + (Δy)² = 20

Step 5 Take the Square Root

d = √20

Simplified: d = 2√5

Decimal: d ≈ 4.472136

d = 2√5 ≈ 4.4721

Step 6 Interpretation

This is the distance from the origin

Also represents the magnitude of vector (2, 4)

|(2, 4)| = 4.4721