Distance between the points (4, 8) and (k,-4) is 13. what is the value of k?
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A ( 4, 8)
B (k, - 4)
By distance formula,
AB = sqrt [ (4 - k)^2 + (8 +4)^2]
=> 13 = sqrt [ 16 + k^2 - 8k + 144]
=> 169 = k^2 - 8k + 160
=> k^2 - 8k - 9 = 0
=> k^2 - 9k +k - 9 = 0
=> k(k-9) + 1(k-9) = 0
=> (k-9)(k+1) = 0
k = 9 and - 1
B (k, - 4)
By distance formula,
AB = sqrt [ (4 - k)^2 + (8 +4)^2]
=> 13 = sqrt [ 16 + k^2 - 8k + 144]
=> 169 = k^2 - 8k + 160
=> k^2 - 8k - 9 = 0
=> k^2 - 9k +k - 9 = 0
=> k(k-9) + 1(k-9) = 0
=> (k-9)(k+1) = 0
k = 9 and - 1
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