Find the value of 'p' for which the points (-1,3) , (2,p) and (5,-1) are collinear.
Hi!
It is given that A (–1, 3), B (2, p) and C (5, –1) are collinear.
Distance between two points (x1, y1) and (x2, y2) is given by
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Again on squaring both the sides
(p2– 6p + 18) (p2+ 2p + 10) = (–p2+ 2p + 12)2
p4 + 2p3 +10p2 – 6p3–12 p2 – 60p +18p2 + 36p +180 = p4 + 4p2 + 144 – 4p3 + 48p – 24p2
p4 – 4p3 +16p2 – 24p +180 = p4 – 4p3 – 20p2 + 48p + 144
36p2 – 72p + 36 = 0
p2 – 2p +1 = 0
(P – 1)2 = 0
p– 1 = 0
p = 1
Cheers!