# Steps on The Coordinate Plane  # Rules

1. A n-step, where n is a positive integer, is a line segment of length $$n$$ and slope $$0$$ or $$undefined$$, or a line segment of length $$n\sqrt{2}$$ and slope of $$1$$ or $$-1$$ . The endpoints of a n-step must be on a lattice point. For example, you may construct a 2-step segment with length of $$2\sqrt{2}$$ and endpoints on $$(2,2)$$ and $$(4,4)$$.

2. Your $$nth$$ construction must be an n-step. For example, your 1st construction must be a 1-step. Your 2nd construction must be a 2-step. Your 14th construction must be a 14-step.

3. For every $$n\geq 2$$, a n-step must share an endpoint with a (n-1)-step.

4. Two n-steps may only intersect at their endpoints.

5. Every lattice point may contain at most two n-steps.

1. On the graph, construct a figure that passes through all lattice points $$(a,b)$$ where $$-3 \leq a \leq 3$$ and $$-3 \leq b \leq 3$$.
2. On the graph, construct a figure that passes through all lattice points $$(a,b)$$ where $$-4 \leq a \leq 3$$ and $$-4 \leq b \leq 3$$.
3. Construct a figure that passes through all lattice points $$(a,b)$$ where $$0 \leq a \leq x$$ and $$0 \leq b \leq y.$$