Question
Question 1
A square has a perimeter of 36 units. One vertex of the square is located at (3,5) on the coordinate grid. What could be another vertex of the square?(1 point)
Responses
(7,5)
(7,5)
(-5,-5)
(-5,-5)
(-3,-9)
(-3,-9)
(9,5)
A square has a perimeter of 36 units. One vertex of the square is located at (3,5) on the coordinate grid. What could be another vertex of the square?(1 point)
Responses
(7,5)
(7,5)
(-5,-5)
(-5,-5)
(-3,-9)
(-3,-9)
(9,5)
Answers
GPT-4o mini
To determine another vertex of the square, we first need to find the length of one side of the square. Given that the perimeter is 36 units, the side length \( s \) of the square can be calculated as follows:
\[
\text{Perimeter} = 4s \implies s = \frac{\text{Perimeter}}{4} = \frac{36}{4} = 9 \text{ units}
\]
Since one vertex of the square is at (3, 5), we can determine possible coordinates of another vertex based on the square's properties.
The vertices of a square can be located in the following directions from a given vertex:
1. Move right (increase x-coordinate) by the side length.
2. Move left (decrease x-coordinate) by the side length.
3. Move up (increase y-coordinate) by the side length.
4. Move down (decrease y-coordinate) by the side length.
Calculating the potential coordinates for the other vertices given the side length of 9:
1. Right: (3 + 9, 5) = (12, 5)
2. Left: (3 - 9, 5) = (-6, 5)
3. Up: (3, 5 + 9) = (3, 14)
4. Down: (3, 5 - 9) = (3, -4)
Since the responses provided include:
- (7,5)
- (-5,-5)
- (-3,-9)
- (9,5)
We can rule out all options except to check for vertices that would maintain the square’s dimensions:
1. **(7, 5)**:
- This is 4 units to the right along the same horizontal line; not valid as it does not represent a vertex of a square.
2. **(-5, -5)**:
- No clear way to get here based on a side of length 9 vertically or horizontally.
3. **(-3, -9)**:
- Also does not maintain horizontal or vertical distance relation for a square.
4. **(9, 5)**:
- This is 6 units to the right; not valid either based on distance.
From our calculations, all offered options do not yield a vertex 9 units away in a correct potential square orientation. However, given the square structure and spacing rules:
- You can express the conditions of a valid square mathematically or geometrically.
Of all given responses, none represent a logical second vertex based on "step-side" square logic from point (3,5) using the condition of side = 9. Typically this indicates an error in question interpretation or option selection for valid square formation. Further correction on this can be necessary in context of definitions or given potential grid configurations.
None of the above provided points are valid choices for another point on the square where one point exists at (3,5) with side length 9 units.
\[
\text{Perimeter} = 4s \implies s = \frac{\text{Perimeter}}{4} = \frac{36}{4} = 9 \text{ units}
\]
Since one vertex of the square is at (3, 5), we can determine possible coordinates of another vertex based on the square's properties.
The vertices of a square can be located in the following directions from a given vertex:
1. Move right (increase x-coordinate) by the side length.
2. Move left (decrease x-coordinate) by the side length.
3. Move up (increase y-coordinate) by the side length.
4. Move down (decrease y-coordinate) by the side length.
Calculating the potential coordinates for the other vertices given the side length of 9:
1. Right: (3 + 9, 5) = (12, 5)
2. Left: (3 - 9, 5) = (-6, 5)
3. Up: (3, 5 + 9) = (3, 14)
4. Down: (3, 5 - 9) = (3, -4)
Since the responses provided include:
- (7,5)
- (-5,-5)
- (-3,-9)
- (9,5)
We can rule out all options except to check for vertices that would maintain the square’s dimensions:
1. **(7, 5)**:
- This is 4 units to the right along the same horizontal line; not valid as it does not represent a vertex of a square.
2. **(-5, -5)**:
- No clear way to get here based on a side of length 9 vertically or horizontally.
3. **(-3, -9)**:
- Also does not maintain horizontal or vertical distance relation for a square.
4. **(9, 5)**:
- This is 6 units to the right; not valid either based on distance.
From our calculations, all offered options do not yield a vertex 9 units away in a correct potential square orientation. However, given the square structure and spacing rules:
- You can express the conditions of a valid square mathematically or geometrically.
Of all given responses, none represent a logical second vertex based on "step-side" square logic from point (3,5) using the condition of side = 9. Typically this indicates an error in question interpretation or option selection for valid square formation. Further correction on this can be necessary in context of definitions or given potential grid configurations.
None of the above provided points are valid choices for another point on the square where one point exists at (3,5) with side length 9 units.