Question
Which set of vertices would create a square that has a side length of 7 units?(1 point)
Responses
(6,8)
, (13,8)
, (13,2)
, (6,2)
left parenthesis 6 comma 8 right parenthesis , left parenthesis 13 comma 8 right parenthesis , left parenthesis 13 comma 2 right parenthesis , left parenthesis 6 comma 2 right parenthesis
(−3,4)
, (4,4)
, (4,−3)
, (−3,−3)
left parenthesis negative 3 comma 4 right parenthesis , left parenthesis 4 comma 4 right parenthesis , left parenthesis 4 comma negative 3 right parenthesis , left parenthesis negative 3 comma negative 3 right parenthesis
(−2,5)
,(−5,5)
, (−5,−2)
, (−2,−2)
left parenthesis negative 2 comma 5 right parenthesis , left parenthesis negative 5 comma 5 right parenthesis , left parenthesis negative 5 comma negative 2 right parenthesis , left parenthesis negative 2 comma negative 2 right parenthesis
(−1,5)
, (7,5)
, (7,−1)
, (−1,−1)
Responses
(6,8)
, (13,8)
, (13,2)
, (6,2)
left parenthesis 6 comma 8 right parenthesis , left parenthesis 13 comma 8 right parenthesis , left parenthesis 13 comma 2 right parenthesis , left parenthesis 6 comma 2 right parenthesis
(−3,4)
, (4,4)
, (4,−3)
, (−3,−3)
left parenthesis negative 3 comma 4 right parenthesis , left parenthesis 4 comma 4 right parenthesis , left parenthesis 4 comma negative 3 right parenthesis , left parenthesis negative 3 comma negative 3 right parenthesis
(−2,5)
,(−5,5)
, (−5,−2)
, (−2,−2)
left parenthesis negative 2 comma 5 right parenthesis , left parenthesis negative 5 comma 5 right parenthesis , left parenthesis negative 5 comma negative 2 right parenthesis , left parenthesis negative 2 comma negative 2 right parenthesis
(−1,5)
, (7,5)
, (7,−1)
, (−1,−1)
Answers
GPT-4o mini
To check which set of vertices forms a square with a side length of 7 units, we can calculate the distances between the vertices in each option.
1. **Set 1:** (6,8), (13,8), (13,2), (6,2)
- Distance between (6,8) and (13,8): \( \sqrt{(13-6)^2 + (8-8)^2} = \sqrt{7^2} = 7 \)
- Distance between (13,8) and (13,2): \( \sqrt{(13-13)^2 + (8-2)^2} = \sqrt{6^2} = 6 \) (not a square)
- **Not a square.**
2. **Set 2:** (−3,4), (4,4), (4,−3), (−3,−3)
- Distance between (−3,4) and (4,4): \( \sqrt{(4+3)^2 + (4-4)^2} = \sqrt{7^2} = 7 \)
- Distance between (4,4) and (4,−3): \( \sqrt{(4-4)^2 + (4+3)^2} = \sqrt{7^2} = 7 \)
- Distance between (4,−3) and (−3,−3): \( \sqrt{(-3-4)^2 + (-3+3)^2} = \sqrt{7^2} = 7 \)
- Distance between (−3,−3) and (−3,4): \( \sqrt{(-3+3)^2 + (4+3)^2} = \sqrt{7^2} = 7 \)
- **This does form a square of side length 7.**
3. **Set 3:** (−2,5), (−5,5), (−5,−2), (−2,−2)
- Distance between (−2,5) and (−5,5): \( \sqrt{(-5+2)^2 + (5-5)^2} = \sqrt{3^2} = 3 \) (not a square)
- **Not a square.**
4. **Set 4:** (−1,5), (7,5), (7,−1), (−1,−1)
- Distance between (−1,5) and (7,5): \( \sqrt{(7+1)^2 + (5-5)^2} = \sqrt{8^2} = 8 \) (not a square)
- **Not a square.**
Thus, the only set of vertices that forms a square with a side length of 7 units is **Set 2:** (−3,4), (4,4), (4,−3), (−3,−3).
1. **Set 1:** (6,8), (13,8), (13,2), (6,2)
- Distance between (6,8) and (13,8): \( \sqrt{(13-6)^2 + (8-8)^2} = \sqrt{7^2} = 7 \)
- Distance between (13,8) and (13,2): \( \sqrt{(13-13)^2 + (8-2)^2} = \sqrt{6^2} = 6 \) (not a square)
- **Not a square.**
2. **Set 2:** (−3,4), (4,4), (4,−3), (−3,−3)
- Distance between (−3,4) and (4,4): \( \sqrt{(4+3)^2 + (4-4)^2} = \sqrt{7^2} = 7 \)
- Distance between (4,4) and (4,−3): \( \sqrt{(4-4)^2 + (4+3)^2} = \sqrt{7^2} = 7 \)
- Distance between (4,−3) and (−3,−3): \( \sqrt{(-3-4)^2 + (-3+3)^2} = \sqrt{7^2} = 7 \)
- Distance between (−3,−3) and (−3,4): \( \sqrt{(-3+3)^2 + (4+3)^2} = \sqrt{7^2} = 7 \)
- **This does form a square of side length 7.**
3. **Set 3:** (−2,5), (−5,5), (−5,−2), (−2,−2)
- Distance between (−2,5) and (−5,5): \( \sqrt{(-5+2)^2 + (5-5)^2} = \sqrt{3^2} = 3 \) (not a square)
- **Not a square.**
4. **Set 4:** (−1,5), (7,5), (7,−1), (−1,−1)
- Distance between (−1,5) and (7,5): \( \sqrt{(7+1)^2 + (5-5)^2} = \sqrt{8^2} = 8 \) (not a square)
- **Not a square.**
Thus, the only set of vertices that forms a square with a side length of 7 units is **Set 2:** (−3,4), (4,4), (4,−3), (−3,−3).