Understanding Engineering Mathematics

B.

123456

(i) and (ii) are both at

the origin, O.

p

(viii)

(vi)

(iv)

(v)

(vii)

(iii)

(i)

(ii)

2 p

0

p 2 p 3 p 6

2 p

3

5 p

6

7 p

6

3 p

2

4 p

3

5 p

3

11 p

6

Figure 7.4The points of 7.1.1(B).

7.2.2 Distance between two points

➤

204 221➤

By Pythagoras’ theorem (154

➤

) the distance between the two points (x 1 ,y 1 ), (x 2 ,y 2 )is

d=

√

(x 1 −x 2 )^2 +(y 1 −y 2 )^2

as illustrated in Figure 7.5.
From the diagram:

d^2 =AB^2 =AC^2 +BC^2

=(x 2 −x 1 )^2 +(y 2 −y 1 )^2

Solution to review question 7.12

The distance between the points (x 1 ,y 1 ), (x 2 ,y 2 ), denotedd((x 1 ,y 1 ),

(x 2 ,y 2 ))is