Question

If the distance between (na,nb) and (a,b) is 5 times the distance between (5a,5b) and (2a,2b) then find n

Answer 1

Answer:

$\large\boxed{\sf{n=16}}$

Step-by-step explanation:

Given points are (na, nb) and (a, b)

By distance formula, we have

Distance between these points are

$\sqrt{ {(na - a)}^{2} + {(nb - b)}^{2} }$

Another points are (5a, 5b) and (2a, 2b).

Distance between them are

$\sqrt{ {(5a - 2a)}^{2} + {(5b - 2b)}^{2} }$

According to Question,

$= > \sqrt{ {(na - a)}^{2} + {(nb - b)}^{2} } = 5 \sqrt{ {(3a)}^{2} + {(3b)}^{2} }$

Squarring both sides, we get

$= > {(na - a)}^{2} + {(nb - b)}^{2} = 25( {(3a)}^{2} + {(3b)}^{2} )$

On Comparing both sides, we get

na - a = 15 a

=> n - 1 = 15

=> n = 16

Hence, the value of n = 16