If a line segment is partitioned having ending points (1,4),(7,1) in the ratio of 3:1 then the coordinates will be (25/4,7/4)
Given Ending points (1,4), (7,1) and the ratio 3:1 in which the line segment is divided.
If we are given the ratio m:n and the ending points of the line segment then the coordinates of the point dividing the segment will be (mx2+nx1/m+n,my2+ny1/m+n)
Putting the values of m=3 n=1 x1=1 y1=4 x2=7 and y2=1 we get
Coordinates (x,y)=(3*7+1*1/3+1,3*1+1*4/3+1)
=(21+1/4,3+4/4)
=(22/4,7/4)
Hence the point which is dividing the line segment having ending points (1,4) and (7,1) in the ratio 3:4 is (22/4,7/4).
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