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The equation of line joining (x1,y1) and (x2,y2) is y−y1y2−y1=x−x1x2−x1
Hence equation of line joining (1,3) and (2,7) is
y−37−3=x−12−1 or y−34=x−11
i.e. 4x−4=y−3 or y=4x−1
Solution of equations 3x+y=9 and y=4x−1 gives point of intersection. Putting second equation in first we get
3x+4x−1=9 or x=107 and y=4×107−1=337
i.e. point of intersection is (107,337)
Now distance of (107,337) and (1,3) is
√(107−1)2+(337−3)2=√949+14449=√1537
and distance of (107,337) and (2,7) is
√(107−2)2+(337−7)2=√1649+25649=√2727
and ratio is √153√272=√17×3×3√17×4×4=34
Hence, the line joining the points (1,3) and (2,7) is divided by the line 3x+y=9 in the ratio of 3:4.
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