Everything Maths Grade 10

AB^2 =AC^2 +BC^2

)AB=

√

AC^2 +BC^2

And:

AC=x 2 x 1

BC=y 2 y 1

Therefore:

AB=

√

AC^2 +BC^2

=

√

(x 2 x 1 )^2 + (y 2 y 1 )^2

Therefore to calculate the distance between any two points,(x 1 ;y 1 )and(x 2 ;y 2 ), we use:

distance(d) =

√

(x 1 x 2 )^2 + (y 1 y 2 )^2

Note that(x 1 x 2 )^2 = (x 2 x 1 )^2.

VISIT:

The following video gives two examples of working with the distance formula and shows how to determine

the distance formula.

See video:2GBSatwww.everythingmaths.co.za

Worked example 1: Using the distance formula

QUESTION

Find the distance betweenS(2;5)andQ(7;2).

SOLUTION

Step 1: Draw a sketch

 2 2 4 6

 6

 4

 2

2

T(7;2)

S(2;5)

x

y

Chapter 8. Analytical geometry 289