If the distance between the points (na, nb) and (a, b) is 4 times the distance between the points (5a, 5b) and (a, b), then 'n' is equal to ?
Answers
Answered by
8
n=5(a+b) * 5(a-b) so this is the answer
Riya1510:
no
Answered by
64
Let A (na, nb)
B (a, b)
P (5a,5b)
Q (a,b)
Then using distance formula,
AB = 4 PQ
AB^2 = 16 PQ^2
[(na-a)^2 +(nb-b) ^2]=16 [(5a-a)^2 +(5b-b)^2]
a^2(n-1)^2 +b^2(n-1)^2 =16[ (4a)^2+(4b)^2]
(n-1)^2 (a^2+b^2) =16^2(a^2+b^2)
(n-1)^2=16^2
n-1=+-16
n=+16+1, - 16+1
n=17,-15
B (a, b)
P (5a,5b)
Q (a,b)
Then using distance formula,
AB = 4 PQ
AB^2 = 16 PQ^2
[(na-a)^2 +(nb-b) ^2]=16 [(5a-a)^2 +(5b-b)^2]
a^2(n-1)^2 +b^2(n-1)^2 =16[ (4a)^2+(4b)^2]
(n-1)^2 (a^2+b^2) =16^2(a^2+b^2)
(n-1)^2=16^2
n-1=+-16
n=+16+1, - 16+1
n=17,-15
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