Manipal Entrance Test 2019 Math Paper

Given that equation of lines are
2x−3y=4 ...(i)
and x+y=1
or x+y−1=0 ...(ii)
Now, let any line parallel to x+y−1=0 is given by x+y+λ=0 which passes through (1, 1).
∴1+1+λ=0⇒λ=−2
∴ Required line is x+y−2=0
or x+y=2 ...(iii)
∴ Point of intersection of lines (i) and (iii) is (2,0)
∴ Required distance =√(2−1)2+(0−1)2=√1+1=√2