    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}=(−λ−4λ+1,7λ−6λ+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. ∴7λ−6λ+1=0⇒7λ−6=0 ∴λ=67 So, the required ratio is 6:7 and the point of division M is {−67−467+1,7×67−667+1} i.e., (−347137,6−613137) i.e.,(−3413,0) Hence, the required point of division is (−3413,0).  Suggest Corrections  0      Similar questions  Explore more