Question

if the point (1,2) (-5,6) and (p,-2 ) are collinear, then p =

by distance formula...​

Answer 1

Let the three points be A(1,2),B(-5,6) and C(p,-2).

Since the three points are collinear.

Therefore,

${(bc)}^{2} = {(ab)}^{2} + {(ac)}^{2} \\ {(p - ( - 5))}^{2} + {(6 - ( - 2))}^{2} = {(1 - ( - 5))}^{2} + {(6 - 2)}^{2} + {(p - 1)}^{2} + {( - 2 - 2)}^{2} \\ {(p + 5)}^{2} + {(6 + 2)}^{2} = {(1 + 5)}^{2} + {4}^{2} + {(p -1)}^{2} + {( - 4)}^{2} \\ ( { {p}^{2} + 25 + 10p) +64} = 36 + 16 + 16 + ( {p}^{2} + 1 - 2p) \\ {p}^{2} + 89 + 10p = 69 + {p}^{2} - 2p \\ 20 = - 12p \\ 5 = - 3p \\ therefore \: p = \frac{ - 5}{3}$

Hope it is helpful