Question

If the distance b/w the points (4,k) and (1,0) is 5 , then what can be the possible values of k

Answer 1

We know that the distance formula,

Let the distance between P and Q points

PQ = √(x2 - x1)² + (y2 - y1)²

(5)² = (4-1)² + (k-0)²

25 = (3)² + k²

k² = 25-9

k² = 16

k = ±4

Hope this answer may help you

Answer 2

√(1-4)² +(0-k)²=5
√9+0+k²+0=5
squaring both  side 
9+k²=25
k²=16
k=4