Q21 of 55 Page 1

Point P(x, 4) lies on the line segment joining the points A(-5, 8) and B(4, -10). Find the ratio in which point P divides the line segment AB. Also, find the value of x.


Let P divides AB in a ratio r: 1.


∴ AP : BP = r : 1


Now, coordinates of P will be .


But, coordinates of P are (x, 4).


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


= x and = 4


On solving the second equation, we get:


-10r + 8 = 4r + 4


⇒ 14r = 4


⇒ r = 2/7


Therefore, r :1 will be equal to 2/7 : 1 = 2 : 7


Thus, the point P divides AB into a ratio 2 : 7


Also, on solving the first equation, we get:


4r – 5 = (r + 1)x


⇒ 4(2/7) – 5 = [(2/7) + 1]x


⇒ 8 – 35 = 9x


⇒ - 27 = 9x


⇒ x = - 3


Therefore, the ratio is 2 : 7 and the point P is (- 3, 4).


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