The ratio in which the line segment joining A(6, 3) and B(-2,-5) is divided by the x also find the coordinates of the point of intersection of ab and the x axis
Answers
Answer:
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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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Step-by-step explanation:
Let the required ratio be λ;1. Then, the coordinates of the point of division are,
R(λ+15λ+2,λ+16λ−3)
But, it is a point on x-axis on which y-coordinates of every point is zero.
∴λ+16λ−3=0⇒λ=21
Thus,the required ratio is 21:1or,1:2.
Putting λ=1/2 in the coordinates of R, we find that its coordinates are (3,0)