Question

c a hexagon with exactly 1 pair of perpendicular sides

Explanation:

Step1: Define grid points

Label grid points as $(x,y)$ where $x=1,2,3,4,5$ and $y=1,2,3,4,5$.

Step2: Select perpendicular sides

Choose vertical side: from $(1,1)$ to $(1,2)$ (vertical, slope undefined). Choose horizontal side: from $(1,2)$ to $(2,2)$ (horizontal, slope $0$; perpendicular to vertical).

Step3: Add 4 more vertices

Add vertices $(3,3)$, $(4,2)$, $(4,1)$, $(2,1)$ to form a closed 6-sided figure (hexagon). Verify only the pair $(1,1)$-$(1,2)$ & $(1,2)$-$(2,2)$ is perpendicular.

Step4: Connect vertices in order

Connect points: $(1,1) \to (1,2) \to (2,2) \to (3,3) \to (4,2) \to (4,1) \to (2,1) \to (1,1)$

Answer:

A valid hexagon is formed by connecting the grid points in this order: $(1,1)$, $(1,2)$, $(2,2)$, $(3,3)$, $(4,2)$, $(4,1)$, $(2,1)$ (and back to $(1,1)$). This shape has exactly one pair of perpendicular sides (the vertical segment from $(1,1)$ to $(1,2)$ and the horizontal segment from $(1,2)$ to $(2,2)$).