formulas used in coordinate geometry

Distance between two points

Let P (x₁, y₁) and Q (x₂, y₂) be the two points. We have to find PQ.

OM = x₁, PM = y₁ = RN

ON = x₂, QN = y₂

PR = MN = ON – OM

= x₂ – x₁

QR = QN – RN = y₂ – y₁

By Pythagoras theorem

PQ² = PR² + QR²

= (x₂ - x₁)² + (y₂ – y₁)²

If x₁ = 0, y₁ = 0, x₂ = x and y₂ = y

Then 

Section Formula

Let P (x, y) divided a line AB such that AP : PB = m₁ : m₂.

Let coordinates of A are (x₁, y₁) and B are (x₂, y₂).

It is obvious that

Taking, 

Similarity 

Note

(i) if P is mid point of AB, then AP : PB = 1 : 1

(ii) If m₁ : m₂ = k, then coordinates of P are