Question

If A (-1,3),B (2,p) , C (5,-1) are collinear, then the value of p is ​

Answer 1

Answer:

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

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