Make constructions for each of the following. Remember this: A construction is a method that should produce the desired outcome any time the given conditions are met. So, making a construction that only works for special cases is not acceptable. Your method must work for any potential situation as long as that situation meets the given conditions.

Explain your constructions so that their logic is clear. Refer to types of explanations (geometry) for a reminder of what this means.

1. Given: Point A, point B and a length m.
Construct the locus of points X such that the m= Dist(X,A) + Dist(X,B).

That is, construct the locus of points such that m is the the sum of any point's distances from A and B.

2. Given: Point A, point B and a length m.
Construct the locus of points X such that the m= Dist(X,A) - Dist(X,B).

That is, construct the locus of points such that m is the difference of any point's distances from A and B.

3. Given: Point A and line k.
Construct the locus of points X such that Dist(X,A) = Dist(X,k).

4. Given segments of length a and b.

5. Given: Point A, line k, and length m.
Construct the locus of points X such that m = Dist(X,A) + Dist(X,k)

6. Given: Point A, line k, and length m.
Construct the locus of points X such that m = Dist(X,A) - Dist(X,k)