Vector DA plus vector DC=m times vector DB(m belongs to r)

It can be proved that the triangle ABC is an isosceles triangle or a right triangle (that is, AB=BC or ∠ B = 90) (do you know this? )

Then when A, B and C can form a triangle (not in a straight line) and the vertical coordinates of A and C are equal (AB=BC).

match condition

That is, the ordinate of a and c is equal, but not equal to the ordinate of B.

A has four choices, and B has three choices after choosing A.

* * * There are 12 kinds.

So there are 12 functions.