Question

17. Determine, by distance formula, whether the points are collinear or not
(i) (1, 2), (5,3) and (18,6)
(ii) (4,3), (5, 1) and (1,9)
(iii) (2,5),(-1,2) and (4,7).
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Answer 1

Step-by-step explanation:

1) Let points A=(1,2) ,B=(5,3)& C= (18,6)

Slope of line AB= 3-2/5-1

= 1/4

Slope of line BC= 6-3/18-5

=3/13

Slope of line AC= 6-2/18-1

= 4/17

THEY ARE NOT COLLINEAR

2) Let points A=(4,3) ,B=(5,1) & C = (1,9)

Slope of line AB= 1-3/5-4

= -2

Slope of line BC = 9-1/1-5

= 8/-4 = -2

Slope of line AC= 9-3/1-4

= 6/-3 = -2

THEY ARE COLLINEAR

3) Let points A=(2,5) ,B=(-1,2) & C=(4,7)

Slope of line AB= 2-5/-1-2

= -3/-3=1

Slope of line AC= 7-5/4-2

=2/2=1

Slope of line BC= 7-2/4+1

=1

THEY ARE COLLINEAR