Distance formula rule, formula for the distance d. The distance is always taken to be positive, and it is not a directed distance from A to B. When A and B do not lie on the same horizontal or vertical line.
If A and B lie on a line parallel to one of the coordinate Axis. Then, by the formula 2,The distance AB is the absolute value of the directed distance → AB
Distance formula Proof:
Let A(x ₁, y ₁)and B(x ₂, y ₂) be two point in the plane. We can find distance from the right triangle AQB by using the pathagoras theorem, we have
Distance formula rule
d² = AB² = A Q² + QB² →→→(1)
∣A Q∣ = ∣RS∣ = ∣RO+OS∣
∣RS∣=∣OR+OS∣
= ∣x ₁x ₁∣
∣QB∣= ∣SBSQ∣=∣OMON∣
= ∣y ₁y ₁∣
therefore, (1) can be written in the form
d²= d=(x ₂ x ₁)²+(y ₂ y ₁)²

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