Let K be a subfield of the field C of constructible numbers

Let K be a subfield of the field C of constructible numbers.

Show that if = (r, s) is the intersection of the vertical line x = a and the line y = mx + b, where a, b, m K, then r and s are in K.

Solution

the 2 line equations are x=a, y=mx+b

putting 1st equation in the 2nd equation, y=ma +b !

So, intersection of the given 2 lines is (a, ma+b)

Now, its given that (a,b,m belong to K ) which implies that ma+b also belongs to K

So, r and s which correspond to a and ma+b respectively are in K.