if the distance between (na,nb) & (a,b) is three times the distance between (4a,4b) and (a,b). Show that n is 10 or -8

Let Ana,nb and Ba,b be the given points. AB = na-a2+nb-b2 = a2n-12+b2n-12 = a2+b2n-12Let C4a,4b and Da,b be the given points.CD = 4a-a2+4b-b2 = 9a2+9b2 = 3a2+b2Now, AB = 3 CDa2+b2n-12 = 3 × 3a2+b2a2+b2n-12 = 81a2+b2n-12 = 81n-1 = ±9n = 10  or  n = -8

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