Find the ratio in which the point (3, 1) divides the line joining the points (1, -1) and (4, 2).

2 thoughts on “Find the ratio in which the point (3, 1) divides the line joining the points (1, -1) and (4, 2).”

1. Step-by-step explanation:

   Using the section formula, if a point (x,y)divides the line joining the points (x1,y1)and (x2,y2) in the ratio m1:m2, then

   (x,y)=(m1+m2m1x2+m2x1,m1+m2m1y2+m2y1)

   Given that ratio m1:m2=xy

   points A(−5,−4) and B(−2,3)

   Let ratio be

   m2m1=1m

   Therefore,

   x=m1+m2m

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2. Answer:

   Ratio = 2:1

   Step-by-step explanation:

   We know,

   Section Formula = P(x,y) = [tex](\frac{mx_{2}+nx_{1}}{m+n} ,\frac{my_{2}+ny_{1}}{m+n} )[/tex]

   where, P(x,y) = (3,1) ; A[tex](x_{1},y_{1})[/tex]=(1,-1) ; B[tex](x_{2},y_{2})[/tex]=(4,2)

   Let us consider the ratio as k:1

   =>(3,1) = [tex](\frac{4k+1}{k+1} , \frac{2k-1}{k+1} )[/tex]

   On comparing the coordinates ,

   => 3 = [tex]\frac{4k+1}{k+1}[/tex]

   => 3(k+1) = 4k+1

   =>3k+3 = 4k+1

   => 3 -1 = 4k -3k

   => k = 2

   Therefore the ratio is 2:1 .

   Note:

   You can also compare the y-coordinates you’ll get the same answer.

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