Answer :
To determine which set of coordinates, when paired with [tex]$(-3, -2)$[/tex] and [tex]$(-5, -2)$[/tex], forms a square, we need to analyze each set of additional coordinates. The essential properties of a square are equal side lengths and equal diagonals.
1. First Pair: [tex]$(-3,0)$[/tex] and [tex]$(0,-2)$[/tex]:
- Given points: [tex]$(-3, -2)$[/tex], [tex]$(-5, -2)$[/tex]
- Additional points: [tex]$(-3, 0)$[/tex], [tex]$(0, -2)$[/tex]
2. Second Pair: [tex]$(-3,0)$[/tex] and [tex]$(-5,0)$[/tex]:
- Given points: [tex]$(-3, -2)$[/tex], [tex]$(-5, -2)$[/tex]
- Additional points: [tex]$(-3, 0)$[/tex], [tex]$(-5, 0)$[/tex]
3. Third Pair: [tex]$(0,-2)$[/tex] and [tex]$(0,-3)$[/tex]:
- Given points: [tex]$(-3, -2)$[/tex], [tex]$(-5, -2)$[/tex]
- Additional points: [tex]$(0, -2)$[/tex], [tex]$(0, -3)$[/tex]
To check if these points form a square, we measure the distances between all pairs of points in each set. But let's evaluate based on the geometric relationship and properties mathematically.
After evaluating all sets of coordinates:
- Set 1: [tex]$(-3, 0)$[/tex] and [tex]$(0, -2)$[/tex] does not form a square.
- Set 2: [tex]$(-3, 0)$[/tex] and [tex]$(-5, 0)$[/tex] does not form a square.
- Set 3: [tex]$(0, -2)$[/tex] and [tex]$(0, -3)$[/tex] does not form a square.
None of these sets, when paired with [tex]$(-3, -2)$[/tex] and [tex]$(-5, -2)$[/tex], result in a square. Therefore, there isn't a set of the given coordinates that can produce a square with the initial two points.
The answer is:
[tex]\[ \boxed{\text{None}} \][/tex]
1. First Pair: [tex]$(-3,0)$[/tex] and [tex]$(0,-2)$[/tex]:
- Given points: [tex]$(-3, -2)$[/tex], [tex]$(-5, -2)$[/tex]
- Additional points: [tex]$(-3, 0)$[/tex], [tex]$(0, -2)$[/tex]
2. Second Pair: [tex]$(-3,0)$[/tex] and [tex]$(-5,0)$[/tex]:
- Given points: [tex]$(-3, -2)$[/tex], [tex]$(-5, -2)$[/tex]
- Additional points: [tex]$(-3, 0)$[/tex], [tex]$(-5, 0)$[/tex]
3. Third Pair: [tex]$(0,-2)$[/tex] and [tex]$(0,-3)$[/tex]:
- Given points: [tex]$(-3, -2)$[/tex], [tex]$(-5, -2)$[/tex]
- Additional points: [tex]$(0, -2)$[/tex], [tex]$(0, -3)$[/tex]
To check if these points form a square, we measure the distances between all pairs of points in each set. But let's evaluate based on the geometric relationship and properties mathematically.
After evaluating all sets of coordinates:
- Set 1: [tex]$(-3, 0)$[/tex] and [tex]$(0, -2)$[/tex] does not form a square.
- Set 2: [tex]$(-3, 0)$[/tex] and [tex]$(-5, 0)$[/tex] does not form a square.
- Set 3: [tex]$(0, -2)$[/tex] and [tex]$(0, -3)$[/tex] does not form a square.
None of these sets, when paired with [tex]$(-3, -2)$[/tex] and [tex]$(-5, -2)$[/tex], result in a square. Therefore, there isn't a set of the given coordinates that can produce a square with the initial two points.
The answer is:
[tex]\[ \boxed{\text{None}} \][/tex]
