Distance from (1, 1) to (4, 7)
Calculate the distance between points (1, 1) and (4, 7) using the distance formula.
Answer:
Distance = d = 3√5 ≈ 6.708204
Step-by-Step Solution
Step 1
Identify the Points
Point 1: P₁(1, 1)
Point 2: P₂(4, 7)
P₁(1, 1), P₂(4, 7)
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 - 1 = 3
Δy = y₂ - y₁ = 7 - 1 = 6
Δx = 3, Δy = 6
Step 4
Square the Differences
(Δx)² = (3)² = 9
(Δy)² = (6)² = 36
Sum = 9 + 36 = 45
(Δx)² + (Δy)² = 45
Step 5
Take the Square Root
d = √45
Simplified: d = 3√5
Decimal: d ≈ 6.708204
d = 3√5 ≈ 6.7082