Find the ratio in which the point P (11,y) divides the line segment joining the points `A(15,5) and B(9,20).` Also find the value of y.

Explanation

Let the required ratio be k: 1.
Then, by the section formula, the coordinates of P are `P((9k +15)/(k +1), (20k+5)/(k+1)).`
But, this point is given as P(11, y).
`therefore (9k +15)/(k+1) = 11 rArr 9k +15 = 11k + 11 rArr 2k = 4 rArr k = 2.`
So, the required ratio is 2:1.
Putting k = 2 in P, we get
`y = (20 xx 2 +5 )/((2+1)) = (45)/(3) = 45.`
Hence, y = 15.