Question

11. Plot the points P(-1,-1), Q(2, 3) and R(8, 11). Showthat they are collinear.​

Answer 1

Answer:

Let point (−2,3,5),(1,2,3)and(7,0,−1) be denoted by P , Q , and R respectively.

by using distance formula d=

(x 2 −x 1 )

2+(y 2−y 1)

2+(z 1−z1 )2

Point P,Q and R are collinear if they lie on a line.

PQ=

(1+2)

2

+(2−3)

2+(3−5) 2

= (3) 2

+(−1) 2

+(−2) 2

= 9+1+4

= 14

QR= (7−1)

2

+(0−2)

2 +(−1−3) 2

= (6) 2

+(−2)

2+(−4) 2

= 36+4+16

=214

PR= (7+2) 2 +(0−3) 2 +(−1−5) 2

= (9)

2+(−3)

2 +(−6) 2= 81+9+36

=314

Hence,

PQ+QR=RP

= 14 +214 =314

the point are collinear