Answer :
Let's analyze each set of vertices step by step to determine which set forms a parallelogram.
### Option A: [tex]\((2,4), (3,3), (6,4), (5,6)\)[/tex]
- This set does not form a parallelogram because the opposite sides are neither parallel nor equal in length.
### Option B: [tex]\((2,3), (5,1), (4,1)\)[/tex]
- This set does not have enough vertices to form a parallelogram. A parallelogram must be defined by exactly four vertices.
### Option C: [tex]\((-5,-2), (-3,3), (3,5), (1,0)\)[/tex]
- This set does form a parallelogram. The opposite sides are parallel and equal in length.
### Option D: [tex]\((-1,2), (1,3), (5,3), (1,1)\)[/tex]
- This set does not form a parallelogram because the opposite sides are neither parallel nor equal in length.
Thus, the correct answer is:
C. [tex]\((-5,-2), (-3,3), (3,5), (1,0)\)[/tex]
### Option A: [tex]\((2,4), (3,3), (6,4), (5,6)\)[/tex]
- This set does not form a parallelogram because the opposite sides are neither parallel nor equal in length.
### Option B: [tex]\((2,3), (5,1), (4,1)\)[/tex]
- This set does not have enough vertices to form a parallelogram. A parallelogram must be defined by exactly four vertices.
### Option C: [tex]\((-5,-2), (-3,3), (3,5), (1,0)\)[/tex]
- This set does form a parallelogram. The opposite sides are parallel and equal in length.
### Option D: [tex]\((-1,2), (1,3), (5,3), (1,1)\)[/tex]
- This set does not form a parallelogram because the opposite sides are neither parallel nor equal in length.
Thus, the correct answer is:
C. [tex]\((-5,-2), (-3,3), (3,5), (1,0)\)[/tex]