Question

apply the Pythagorean theorem to find the length between the two points. the points are (7,8)and (3,2)

Answer 1

To find the distance between two points using the Pythagorean theorem, we need to determine the length of the two sides of a right triangle formed by the two points. Here's how we can do it:

Let's denote the two points as A (7, 8) and B (3, 2).

1. Find the horizontal difference (Δx):
Δx = x₂ - x₁
Δx = 3 - 7
Δx = -4

2. Find the vertical difference (Δy):
Δy = y₂ - y₁
Δy = 2 - 8
Δy = -6

3. Square both the Δx and Δy values:
Δx² = (-4)² = 16
Δy² = (-6)² = 36

4. Apply the Pythagorean theorem:
distance² = Δx² + Δy²
distance² = 16 + 36
distance² = 52

5. Take the square root of both sides to find the distance:
distance = √52
distance ≈ 7.211

Therefore, the distance between the two points (7, 8) and (3, 2) is approximately 7.211 units.