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Which set of vertices forms a parallelogram?

A. [tex]\( A(2,4), B(3,3), C(6,4), D(5,6) \)[/tex]

B. [tex]\( A(-1,1), B(2,4), C(5,1), D(4,1) \)[/tex]

C. [tex]\( A(-5,-2), B(-3,3), C(3,5), D(1,0) \)[/tex]

D. [tex]\( A(-1,2), B(1,3), C(5,3), D(1,1) \)[/tex]

Sagot :

GinnyAnswer
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]
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