Answer the given question with proper steps.
Q.15. Find the ratio in which 2x - 3y + 5 = 0 divides the line segment joining (1, 3) and (5, 4).

Dear student
Let the coordinates be P(x,y).Let the ratio be m:n in which the line 2x-3y+5=0divides the line segment joining the points (1,3) and (5,4)Since this point P lies on the line joining the points (1,3) and (5,4) and divide the line segment in the ratio m:n.So, the co-ordinates of point P arex=5m+nm+n and y=4m+3nm+n     [By section formula]Since this point P also lies on the given line 2x-3y+5=0,so it must satisfy the equation of this line.So,25m+nm+n-34m+3nm+n+5=010m+2n-12m-9n+5m+5n=03m-2n=0mn=23Hence m:n=2:3
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LET THE RATIO BE K:1 NOW  BY FORMULA
X=M1X2M2X1/M1+M2
=5K+1/K+1.... 1ST EQ

NOW 
Y=M1Y2M2Y1/M1+M2
  =4K+3/K+1.. 2ND EQ


PUTTING VALUE OF 1ST AND 2ND IN GIVEN EQUATION
WE GET 5K+1+4K+3/K+1
        NOW AFTER SOLUTION K=4/9
SO RATIO IS 4:9
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I hope it will be helpful....

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