Find the distance between each pair of points: 1. ( -4, 6) and ( 3, -7)
2. ( -6, -5) and (2,0)
3. ( -1, 4) and ( 1, -1)
4. ( 0, -8) and (3, 2)

The distance between points P(x

1

,y

1

,z

1

) and Q(x

2

,y

2

,z

2

) is given by

PQ=

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

+(z

2

−z

1

)

2

(i) Distance between points (2,3,5) and (4,3,1)

=

(4−2)

2

+(3−3)

2

+(1−5)

2

=

(2)

2

+(0)

2

+(−4)

2

=

4+16

=

20

= 2

5

(ii) Distance between points (−3,7,2) and (2,4,−1)

=

(2+3)

2

+(4−7)

2

+(−1−2)

2

=

(5)

2

+(−3)

2

+(−3)

2

=

25+9+9

=

43

(iii) Distance between points (−1,3,−4) and (1,−3,4)

=

(1+1)

2

+(−3−3)

2

+(4+4)

2

=

(2)

2

+(−6)

2

+(8)

2

=

4+36+64

=

104

=2

26

(iv) Distance between points (2,−1,3) and (−2,1,3)

=

(−2−2)

2

+(1+1)

2

+(3−3)

2

=

(−4)

2

+(2)

2

+(0)

2

=

16+4

=

20

= 2

5

mx+89b(-98)nb

step-by-step explanation: