Question

If a ( 6, -1) b (1, 3)c (k, 8) three points such that ab=bc find the valie of ak

Answer 1

Distance formula: Distance between to points P(x₁, y₁) and Q(x₂, y₂) is √[(x₂-x₁)²+(y₂-y₁)²]

Given that

ab = bc

⇒ ab² = bc²       [ squaring on both side ]

⇒ [(1-6)²+(3+1)²] = [(k-1)²+(8-3)²]         [ using distance formula ]

⇒ 25+16 = k²+1-2k+25

⇒ k²-2k-15 = 0

⇒ k²+3k-5k-15 = 0

⇒ k(k+3)-5(k+3) = 0

⇒ (k+3)(k-5) = 0

⇒  k+3 = 0    or k-5 = 0

⇒ k = -3    or k = 5

Answer 2

Answer:

$k= 5 \: or - 3$

Step-by-step explanation:

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