Question

Which set of vertices would create a square that has a side length of 5 units?(1 point)
Responses

(−1,4)
, (−1,−1)
, (4,−1)
, (4,4)
left parenthesis negative 1 comma 4 right parenthesis , left parenthesis negative 1 comma negative 1 right parenthesis , left parenthesis 4 comma negative 1 right parenthesis , left parenthesis 4 comma 4 right parenthesis

(−3,4)
, (2,4)
, (2,7)
, (−3,7)
left parenthesis negative 3 comma 4 right parenthesis , left parenthesis 2 comma 4 right parenthesis , left parenthesis 2 comma 7 right parenthesis , left parenthesis negative 3 comma 7 right parenthesis

(4,4)
, (9,4)
, (9,0)
, (4,0)
left parenthesis 4 comma 4 right parenthesis , left parenthesis 9 comma 4 right parenthesis , left parenthesis 9 comma 0 right parenthesis , left parenthesis 4 comma 0 right parenthesis

(−6,1)
, (−1,1)
, (−1,−6)
, (−6,−6)

Answer 1

To determine which set of vertices creates a square with a side length of 5 units, we can analyze each set of vertices based on the distance between the points.

### Check each set of vertices:

1. **Set 1: (−1,4), (−1,−1), (4,−1), (4,4)**
- Distance between (−1,4) and (−1,−1): \( |4 - (-1)| = 5 \) (vertical side)
- Distance between (−1,−1) and (4,−1): \( |4 - (-1)| = 5 \) (horizontal side)
- Each side measures 5 units — this set forms a square.

2. **Set 2: (−3,4), (2,4), (2,7), (−3,7)**
- Distance between (−3,4) and (−3,7): \( |7 - 4| = 3 \) (vertical side)
- Distance between (−3,4) and (2,4): \( |2 - (-3)| = 5 \) (horizontal side)
- Not all sides are equal — this does not form a square.

3. **Set 3: (4,4), (9,4), (9,0), (4,0)**
- Distance between (4,4) and (9,4): \( |9 - 4| = 5 \) (horizontal side)
- Distance between (9,4) and (9,0): \( |4 - 0| = 4 \) (vertical side)
- Not all sides are equal — this does not form a square.

4. **Set 4: (−6,1), (−1,1), (−1,−6), (−6,−6)**
- Distance between (−6,1) and (−1,1): \( |−1 - (−6)| = 5 \) (horizontal side)
- Distance between (−6,1) and (−6,−6): \( |1 - (−6)| = 7 \) (vertical side)
- Not all sides are equal — this does not form a square.

### Conclusion:
The only set of vertices that forms a square with a side length of 5 units is:

**Set 1: (−1,4), (−1,−1), (4,−1), (4,4)**