Question

If the points (1, 2) (-5,6) and (p, -2)
are collinear, then p







​

Answer 1

Answer:

let the points be A(1,2) , B(-5,6) , C(p,-2)

if the points are collinear then AB = BC

$\sqrt{ {(1 - ( - 5))}^{2} + ( {2 - 6)}^{2} } = \sqrt{ {( - 5 - p)}^{2} + {(6 - ( - 2)}^{2} } \\ = > \sqrt{ {6 }^{2} + { (- 4)}^{2} } = \sqrt{25 + 10p + {p}^{2} + {8}^{2} } \\ = > \sqrt{36 + 16} = \sqrt{ {p}^{2} + 10p + 25 + 89 } \\ = > \sqrt{52} = \sqrt{ {p}^{2} + 10p + 114 } \\ = > 52 = {p}^{2} + 10p + 114 \\ = > {p}^{2} + 10p + 114 - 52 = 0 \\ = > {p}^{2} + 10p + 62 = 0 \\ =$

by distance formula we get this..solve the last equation you will find the answer