Geometric Proofs on the Cartesian Plane
Cartesian Coordinate Plane
A(-2, 1)B(4, 5)
Point A (x₁, y₁):
Point B (x₂, y₂):
Distance & Pythagorean Relationship
Horizontal Δx = x₂ − x₁:
4 − (-2) = 6 (Δx² = 36)
Vertical Δy = y₂ − y₁:
5 − (1) = 4 (Δy² = 16)
Distance d = √(Δx² + Δy²):
d = √(36 + 16) = 7.211
The distance formula is simply the Pythagorean theorem $a^2 + b^2 = c^2$ applied to the horizontal and vertical legs of the right triangle formed between coordinates A and B.
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