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Question

In what ratio does the X-axis divide the line segment joining the points (-4,-6) and (-1,7)? Find the coordinates of the points of division.


A

(3413,0).

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B

(3013,0).

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C

(3412,1).

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D

(3215,0).

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Solution

The correct option is B

(3413,0).


Let the required ratio be λ:1

So, the coordinates of the point M of division A(-4,-6) and B(-1,7) are

(λx2+1.x1λ+1,λy2+1.y1λ+1)

Here, x1=4,x2=1 and y1=6,y2=7

i.e.,{λ(1)+1(4)λ+1,λ(7)+1(6)λ+1}=(λ4λ+1,7λ6λ+1)

But according to the question, line segment joining A(-4,-6) and B(-1,7) is divided by the X-axis.

So, y-coordinate must be zero.

7λ6λ+1=07λ6=0

λ=67

So, the required ratio is 6:7 and the point of division M is

{67467+1,7×67667+1}

i.e., (347137,6613137) i.e.,(3413,0)

Hence, the required point of division is (3413,0).


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