The ratio by which the line 2x+5y−7=0 divides the straight line joining the points (−4,7) and (6,−5) is
A
1:4
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B
1:2
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C
1:1
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D
2:3
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E
1:3
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Solution
The correct option is D1:1
Using the section formula, if a point (x,y) divides the line joining the points (x1,y1) and (x2,y2) in the ratio m:n, then (x,y)=(mx2+nx1m+n,my2+ny1m+n)
Let the line 2x+5y−7=0 divide the straight line joining points (−4,7) and (6,−5) in the ratio m:n, then the point of intersection by Section Formula is (−4m+6nm+n,7m−5nm+n)
Since the intersection point lies on the given line, we have 2×(−4m+6nm+n)+5×(7m−5nm+n)−7=0