Everything Maths Grade 10

8.2 Distance between two points EMA69

A point is a simple geometric object having location as its only property.

DEFINITION: Point

A point is an ordered pair of numbers written as(x;y).

DEFINITION: Distance

Distance is a measure of the length between two points.

Investigation: Distance between two points

PointsP(2; 1),Q(2;2)andR(2;2)are given.

• Can we assume thatR^= 90°? If so, why?


• Apply the theorem of Pythagoras in△P QRto find the length ofP Q.

 2  1 1 2

 2

 1

1

2

R(2;2)

P(2; 1)

Q(2;2)

x

y

To derive a general formula for the distance between two pointsA(x 1 ;y 1 )andB(x 2 ;y 2 )we use the theorem
of Pythagoras.

 2  1 1 2

 2

 1

1

2

C(x 2 ;y 1 )

B(x 2 ;y 2 )

A(x 1 ;y 1 )

x

y

288 8.2. Distance between two points