Everything Maths Grade 10

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

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

x 1 = 3 y 1 = 9 x 2 = 8 y 2 =y

Step 3: Write down the distance formula

d=

√

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

Step 4: Substitute values and solve fory

13 =

√

(38)^2 + (9y)^2

132 = (5)^2 +

(

81  18 y+y^2

)

0 =y^2  18 y 63

= (y+ 3) (y21)

)y= 3 ory= 21

Step 5: Check both values fory

Checky= 3 :

d=

√

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

=

√

(38)^2 + (9 + 3)^2

=

p

25 + 144

=

p

169

= 13

Checky= 21:

d=

√

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

=

√

(38)^2 + (921)^2

=

p

25 + 144

=

p

169

= 13

Step 6: Write the final answer

Sis(8;3)or(8; 21).

Thereforey= 3 ory= 21.

NOTE:

Drawing a sketch helps with your calculation and makes it easier to check if your answer is correct.

Chapter 8. Analytical geometry 291