In what ratio is the line joining the points `(2,3)a n d(4,1)` divides the segment joining the points`(1,2)a n d(4,3)?`

Explanation

Let `P(2,3),Q(4,1),R(1,2),S(4,3)` be the points

Equation of` PQ:(y−1)/(x-4)​=(2)/(-2)⇒x+y=5 ___ (1)`

Equation of RS:`(y−3)/(x-4)​=1/3​⇒3y−x=5......(2)`

Adding `(1), (2)`, `4y=10⇒y=5/2,x=5/2`

`x(5/2​,5/2​)` is the point of intersection

Let x divide RS in m:1 ratio, then

`(3m+2(1)​)/(m+1)=5/2[(my_2​+ny_1)/(m+n)​​=y]`

`6m+4=5m+5`

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