Question

Find the value of k for which the distance between (9, 2) & (3, k) is 10 units

Answer 1

you can use distance formula for that sum let A(9,2) B(3,k)
distance AB=√(3-9)²+(k-2)²
100=36+k²-4k+4
100-36=k²-4k+4
60= k²-4k
k²-10k+6k-60=0
k(k-10)+6(k-10)=0
(k-10)(k+6)=0
k=10 or. k= -6

Answer 2

Let A(9,2) and B(3,k)

AB = 10 
⇒ √(x1-x2)² + (y1-y2)² =10
⇒√36 + 4 + k² - 4k = 10
⇒k²-4k+40 = 100
⇒k²-4k-60 = 0
⇒k²-10k +6k -60 = 0
⇒k(k-10)-6(k-10) = 0

⇒k=10 or
k=6