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.

Find the ratio in which the point P (11,y) divides the line segment jo

1.	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.
Answer» 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.

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