(1) if Z₁ = (mZ₂+Z₃)/m+1 where m belong to real no., then the distance of Z₁ from the line joining the points

Z₂ and Z_3.

ans=0

z1 is the point thats dividing z2 n z3 in ratio 1:m

so it lies on that line (joining z2 n z3)

so the dist frm z1 to the line =0

what asish is correct

also on solving we get

m=(z₃-z₁)/(z₁-z₂)

which gives the slope of the line on which z₁,z₂,z₃ lie

and since m is real

therefore the pts r collinear.