Question
A square has an area of 9 units. One vertex of the square is located at (3,6). Which of the following could be the coordinates of another possible vertex?(1 point)
Responses
(6,9)
(6,9)
(3,-3)
(3,-3)
(6,0)
(6,0)
(0,6)
Responses
(6,9)
(6,9)
(3,-3)
(3,-3)
(6,0)
(6,0)
(0,6)
Answers
GPT-4o mini
Given that the area of the square is 9 square units, the side length of the square is \( \sqrt{9} = 3 \) units.
For a square with one vertex at (3, 6), the possible coordinates for the other vertices can be determined by moving 3 units in the horizontal and/or vertical directions.
The coordinates of the vertices can be:
1. Moving 3 units to the right (increase x-coordinate):
- (3 + 3, 6) = (6, 6)
2. Moving 3 units to the left (decrease x-coordinate):
- (3 - 3, 6) = (0, 6)
3. Moving 3 units up (increase y-coordinate):
- (3, 6 + 3) = (3, 9)
4. Moving 3 units down (decrease y-coordinate):
- (3, 6 - 3) = (3, 3)
Additionally, the diagonal move can create other vertices at equal distances:
5. Moving diagonally down to the right (3 units horizontally and 3 units vertically):
- (3 + 3, 6 - 3) = (6, 3)
6. Moving diagonally down to the left:
- (3 - 3, 6 - 3) = (0, 3)
7. Moving diagonally up to the left:
- (3 - 3, 6 + 3) = (0, 9)
8. Moving diagonally up to the right:
- (3 + 3, 6 + 3) = (6, 9)
Now, let's examine the given options for other possible vertices:
- (6, 9) – This could be a vertex (diagonal move up).
- (3, -3) – This is not a valid coordinate based on the 3-unit distance.
- (6, 0) – This is also not valid based on the original vertex.
- (0, 6) – This could be a vertex obtained by moving left.
From the provided options, **the coordinates (6, 9)** and **(0, 6)** could potentially be the coordinates of another vertex of the square.
So, **the valid response is (6, 9)**, as it is a correct diagonal vertex.
For a square with one vertex at (3, 6), the possible coordinates for the other vertices can be determined by moving 3 units in the horizontal and/or vertical directions.
The coordinates of the vertices can be:
1. Moving 3 units to the right (increase x-coordinate):
- (3 + 3, 6) = (6, 6)
2. Moving 3 units to the left (decrease x-coordinate):
- (3 - 3, 6) = (0, 6)
3. Moving 3 units up (increase y-coordinate):
- (3, 6 + 3) = (3, 9)
4. Moving 3 units down (decrease y-coordinate):
- (3, 6 - 3) = (3, 3)
Additionally, the diagonal move can create other vertices at equal distances:
5. Moving diagonally down to the right (3 units horizontally and 3 units vertically):
- (3 + 3, 6 - 3) = (6, 3)
6. Moving diagonally down to the left:
- (3 - 3, 6 - 3) = (0, 3)
7. Moving diagonally up to the left:
- (3 - 3, 6 + 3) = (0, 9)
8. Moving diagonally up to the right:
- (3 + 3, 6 + 3) = (6, 9)
Now, let's examine the given options for other possible vertices:
- (6, 9) – This could be a vertex (diagonal move up).
- (3, -3) – This is not a valid coordinate based on the 3-unit distance.
- (6, 0) – This is also not valid based on the original vertex.
- (0, 6) – This could be a vertex obtained by moving left.
From the provided options, **the coordinates (6, 9)** and **(0, 6)** could potentially be the coordinates of another vertex of the square.
So, **the valid response is (6, 9)**, as it is a correct diagonal vertex.