The ratio in which the line joining points A(-1,-1) and B(2,1) divides the line joining C(3,4) and D(1,2)

Step-by-step solution

A(-1,-1), B(2,1) and C(3,4), D(1,2) Then equation of line A B aligned y-y₁ & = y₂-y₁ x₂-x₁ (x-x₁ ) y+1 & = 1+1 2+1 (x+1) or 3 y+3 & =2 x+2 or 2 x-3 y-1=0 aligned Let the line A B divides the line joining C and D in ratio : 1 , then coordinates of P are P= ( +3 +1 , 2 +4 +1 ) Since, point P lies on the line A B , putting it in equation of line A B , we obtain aligned & & 2 ( +3 +1 )-3 ( 2 +4 +1 )-1 & =0 & & 2 +6-6 -12- -1 & =0 & & -5 -7 & =0 & & & =-7 / 5 & & : 1 & =7: 5 aligned Negative sign indicates that line A B