Let P (x, y) , A (x_{1}, y_{1}) and B (x_{2}, y_{2}) and be the given points.

Here, x = k, y = 7, x_{1} = 8, y_{1} = 9, x_{2} = 1, y_{2} = 2,

By Section formula y = (my_{2}+ny_{1})/(m+n)

7 = m×2+n×9/(m+n)

7 = 2m+9n/(m+n)

7m+7n = 2m+9n

7m-2n = 9n-7n

5m = 2n

m/n = 2/5

Hence m:n = 2:5.

By Section formula, x = (mx_{2}+nx_{1})/(m+n)

k = (2×1+5×8)/2+5

k = (2+40)/7

k = 42/7 = 6

Hence value of k is 6.

Hence P(6,7) divides the segment in the ration 2:5.