Everything Maths Grade 10

Step 2: Assign values to(x 1 ;y 1 )and(x 2 ;y 2 )

Let the coordinates ofSbe(x 1 ;y 1 )and the coordinates ofTbe(x 2 ;y 2 ).

x 1 = 2 y 1 = 5 x 2 = 7 y 2 = 2

Step 3: Write down the distance formula

d=

√

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

Step 4: Substitute values

dST=

√

( 2 7)^2 + ( 5 (2))^2

=

√

(9)^2 + (3)^2

=

p

81 + 9

=

p

90

=9,5

Step 5: Write the final answer

The distance betweenSandTis 9,5 units.

Worked example 2: Using the distance formula

QUESTION

GivenRS= 13,R(3; 9)andS(8;y). Findy.

SOLUTION

Step 1: Draw a sketch

 4 4 8 12

 8

 4

4

8

12

16

20

24

R(3; 9)

S 2 (8;y 2 )

S 1 (8;y 1 )

x

y

Note that we expect two possible values fory. This is because the distance formula includes the term(y 1 y 2 )^2
which results in a quadratic equation when we substitute in theycoordinates.

290 8.2. Distance between two points