Q24 of 55 Page 1

Point M(11, y) lies on the line segment joining the points P(15, 50) and Q(9, 20). Find the ratio in which point M divides the line segment PQ. Also find the value of y.


Let M divides PQ in a ratio k : 1.


∴ MP : MQ = k : 1


Now, coordinates of M will be .


But, coordinates of Mare (11, y).


So, equating the x coordinate and y coordinate separately, we get:


= 11 and = y


On solving the first equation, we get:


9k + 15 = 11k + 11


⇒ 2k = 4


⇒ k = 2


Therefore, k :1 will be equal to 2 : 1


Thus, the point M divides PQ into a ratio 2 : 1


Also, on solving the second equation, we get:


20k + 5 = (k + 1)y


⇒ (20 × 2) + 5 = [2 + 1]y


⇒45 = 3y


⇒ y = 15


Therefore, the ratio is 2 : 1 and the point M is (11, 15).


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