Consider two infinite line charges with linear charge densities and respectively, which are lying in -direction as shown in the figure below.

Then, the electric field due to line at the mid way between the two line charges, i.e. at is

… (i)

which lies along +ve -axis (outward), i.e. from to .
Similarly, the electric field due to line at the mid way between the two line charges, i.e. at is

… (ii)

Due to negative charge on also lies along +ve X-axis (inward), i.e. from A to B.
So, the resultant electric field at is given as

Substituting the values from Eqs. (i) and (ii) n eq (iii) we get

Which also lies along the + ve X-axis, i.e. from A to B.