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

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

Answer: Distance = d = 4√2 ≈ 5.656854

Step-by-Step Solution

Step 1 Identify the Points

Point 1: P₁(0, 4)

Point 2: P₂(4, 0)

P₁(0, 4), P₂(4, 0)

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 = 4 - 0 = 4

Δy = y₂ - y₁ = 0 - 4 = -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