Find the ratio in which point p(6, 7) divides the segment joining A(8, 9) and B(1, 2) by completing the following activity.
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Answer:
The ratio in which the point p divide the line segment AB is 2 : 5
Step-by-step explanation:
Given as :
The point = p = x , y = (6 , 7)
The point of line segment AB , A = = (8 , 9)
and B = = (1, 2)
Let the ration in which line segment AB is divided = m : n
According to question
x =
Or, 6 =
Or, 6 m + 6 n = m + 8 n
Or, 6 m - m = 8 n - 6 n
Or, 5 m = 2 n
Or, 5 m - 2 n = 0 ...........A
Again
y =
Or, 7 =
Or, 7 m + 7 n = 2 m + 9 n
Or, 7 m - 2 m = 9 n - 7 n
Or, 5 m = 2 n
Or, 5 m - 2 n = 0 ........B
Solving eq A and eq B
5 m - 2 n = 0
i.e 5 m = 2 n
Or, m : n = 2 : 5
So, The ratio in which the point p divide the line segment = 2 : 5
Hence, The ratio in which the point p divide the line segment AB is 2 : 5 Answer
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