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he line segment joining the points ( 3, 4) and ( K, 2 ) is divided by the line 2x+3y+5=0  in the ratio 2:3 then K=

7 years ago

Answers : (2)

ankitesh gupta
63 Points
							

CLEARLY BY APPLYING SECTION FORMULA WE GET (X,Y)=[{(2K+9)/5},{(4+12)/5}]

SO FROM COMPARING X={(2K+9)/5}, AND Y=16/5

 SINCE C(X,Y) LIES ON THE LINE 2X+3Y+5=0 IT SHOULD SATISFY THE EQUATION SO SUBSTITUTE THE VALUES OF ''X'' AND ''Y'' AND GET THE VALUE OF ''K''

 HOPE IT HELPED YOU IF YES APPROVE IT BY CLICKING THE YES BUTTON...............................Smile

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7 years ago
Aman Bansal
592 Points
							

Dear Akhil,

The equation of the straight line joining the points (6, 8) and (-3, -2) is
y -8 = [(-2 -8)/(-3 -6)](x -6)                                  (Two-point form)
=> y -8 = (10/9) (x -6)   =>  9 y -72 = 10 x -60
=> 10 x -9 y +12 = 0         ...(i)
Let the line joining the points (6, 8) and (-3, -2) i.e. the line (i) divide the line segment joining the points (2, 3) and (4, -5) at the point P in the ratio k : 1, then the co-ordinates of point P are
((k.4 +1.2)/(k+1), (k (-5) +1 .3)/(k+1)) i.e. ((4k +20)/(k+1), (-5k +3)/(k+1))
Since P lies on (i), we get
10[(4k +20)/(k+1)] -9[(-5k +3)/(k+1)] + 12 = 0
=> 40 k +20 +45 k -27 +12 k +12 = 0
=> 97 k +5 = 0 => k = -5/97
Hence the required ratio is -5/97 i.e. 5 : 97 externally.

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6 years ago
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