The distance formula is derived from which theorem?

Class 10Coordinate GeometryGeometry — Coordinates

APythagoras theorem
BThales theorem
CMid-point theorem
DBasic Proportionality theorem

Step-by-Step Solution

The distance √[

(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

] is the hypotenuse of a right triangle with horizontal leg

(x

₂−

x

₁) and vertical leg

(y

₂−

y

₁), so it follows from the Pythagoras theorem.

Answer: A) Pythagoras theorem

Key idea: Distance formula

**Distance** between two points P

(x

₁,

y

₁) and Q

(x

₂,

y

₂):

**PQ =

(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

**

This is just the Pythagoras theorem applied to the right triangle formed with horizontal and vertical legs.

**Example**: Distance between (3, 4) and (7, 1).
=

(7 - 3)^{2} + (1 - 4)^{2} = 16 + 9 = 25 = 5

.

**Special distance from origin**: distance of

(x, y)

from (0, 0) is

x^{2} + y^{2}

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