Find the ratio in which line segment joining the points A (3, -3) and B (-2, 7) is divided by x-axis. Also find the coordinates of the point of division.
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Heya !!
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 ).
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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