solve questions on distance formula

Question

The distance between [5,a]  and[ 9,6] is 4, find a value.

Answer 1

Distance between the points (5,a) (9,6) = 4

sqrt[(9-5)^2+(6-a)^2] = 4

sqrt(16+(6-a)^2) = 4

Squaring on both sides.

16+(6-a)^2 = 16

(a-6)^2 = 0

(a-6)(a-6) = 0

a = 6