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in what ratio does the x axis divide the line segment joining the points (-

in what ratio does the x axis divide the line segment joining the points (-4,-6) and (-1,7) ? find the co ordinates of the point of division

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A)
Let x-axis divides the line segment joining (–4, –6) and (–1, 7) at the point P in the ratio 1 : k.
 
Now, coordinates of point of division P are
 
x coordinate = (-1 - 4k) / (k + 1)
 
y coordinate = (7 - 6k) / (k + 1)
 
Since P lies on x-axis, therefore y coordinate = 0
 
(7 - 6k) / (k + 1) = 0
 
7 - 6k = 0
 
k = 7/6
 
Hence, the ratio is 1:7/6 = 6:7
 
x=(-k-4)/k+1 =((-6/7 -4))/(6/7 +1) =-34/13
 
x=-34/13
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