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# The straight line 3x+y=9 divides the line segment joining the points (1,3) and (2,7) in the ratio (A) 3 : 4 externally (B) 3 : 4 internally (C) 4 : 5 internally (D) 5 : 6 externally

one year ago

The equation of line joining (x1,y1) and (x2,y2) is yy1y2y1=xx1x2x1

Hence equation of line joining (1,3) and (2,7) is

y373=x121 or y34=x11

i.e. 4x4=y3 or y=4x1

Solution of equations 3x+y=9 and y=4x1 gives point of intersection. Putting second equation in first we get

3x+4x1=9 or x=107 and y=4×1071=337

i.e. point of intersection is (107,337)

Now distance of (107,337) and (1,3) is

(1071)2+(3373)2=949+14449=1537

and distance of (107,337) and (2,7) is

(1072)2+(3377)2=1649+25649=2727

and ratio is 153272=17×3×317×4×4=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.

one year ago
The line joining the points (1,3) and (2,7) is divided by the line 3x+y=9 in the ratio of 3:4 …...............................