Question

Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (–1, 6).

Answer 1

Answer:

Let the ratio be k : 1 .

Then by the section formula, the coordinates of the point which divides AB in the ratio k : 1 are

[ (-2k+3) / (k+1) , (7k - 3) / (k+1) ]

The point lies on x-axis, and we know that on the x-axis the ordinate is 0.

Therefore, (7k-3) / (k+1) = 0

=> 7k-3 = 0

=> 7k = 3

=> k = 3/7

=> k : 1 = 3 : 7

Putting the value of k = 3/7, we get point of intersection as

{ [ -2(3/7) + 3] ÷ (3/7)+1 , 0 }

=> { [(-6/7) + 3] ÷ (3/7) + 1 , 0 }

=> [(-6+21)/7 ÷ (3+7)/7 , 0 ]

=> [ 15/7 ÷ 10/7 , 0 ]

=> [ 15/10 , 0 ]

=> ( 3/2 , 0 ).

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Answer 2

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