Alg6.13

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Find the point which divides the line segment joining (-1,2) and (4,-5) in the ratio 3:2

The formula for a point which divides the line joining A(x1,y1) and (x2,y2) in the ratio l:m is

\left({\frac  {lx_{2}+mx_{1}}{l+m}},{\frac  {ly_{2}+my_{1}}{l+m}}\right)\,

Applying the formula,

The point is

\left({\frac  {3\cdot 4+2\cdot (-1)}{3+2}},{\frac  {(3\cdot (-5)+2\cdot 2}{3+2}}\right)\,

\left({\frac  {10}{5}},{\frac  {-11}{5}}\right)\,

Hence the point is (2,-11/5)


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