Question
On a coordinate plane, a square and a point are shown. The square has points R prime (negative 8, 1), S prime (negative 4, 1), T prime (negative 4, negative 3), and U prime (negative 8, negative 3). Point S is at (3, negative 5).
Square RSTU is translated to form R'S'T'U', which has vertices R'(–8, 1), S'(–4, 1), T'(–4, –3), and U'(–8, –3). If point S has coordinates of (3, –5), which point lies on a side of the pre-image, square RSTU?
(–5, –3)
(3, –3)
(–1, –6)
(4, –9)
Square RSTU is translated to form R'S'T'U', which has vertices R'(–8, 1), S'(–4, 1), T'(–4, –3), and U'(–8, –3). If point S has coordinates of (3, –5), which point lies on a side of the pre-image, square RSTU?
(–5, –3)
(3, –3)
(–1, –6)
(4, –9)
Answers
Answered by
GPT-4o mini
To find which point lies on a side of the pre-image square \( RSTU \) with vertices \( R(-8, 1) \), \( S(-4, 1) \), \( T(-4, -3) \), and \( U(-8, -3) \), we first need to identify the coordinates of the sides of the square.
The sides of the square are as follows:
1. From \( R(-8, 1) \) to \( S(-4, 1) \): This side is horizontal at \( y = 1 \) between \( x = -8 \) and \( x = -4 \).
2. From \( S(-4, 1) \) to \( T(-4, -3) \): This side is vertical at \( x = -4 \) between \( y = 1 \) and \( y = -3 \).
3. From \( T(-4, -3) \) to \( U(-8, -3) \): This side is horizontal at \( y = -3 \) between \( x = -4 \) and \( x = -8 \).
4. From \( U(-8, -3) \) to \( R(-8, 1) \): This side is vertical at \( x = -8 \) between \( y = -3 \) and \( y = 1 \).
Now, we need to check the possible coordinates given in the options to see which point lies on one of these sides:
1. **Point**: \( (-5, -3) \)
- This point is not on the side since \( x = -5 \) is not in the range of \( x = -8 \) and \( x = -4 \) for \( y = -3 \).
2. **Point**: \( (3, -3) \)
- This point is also not on the side since \( x = 3 \) is not in the range of \( x = -8 \) and \( x = -4 \) for \( y = -3 \).
3. **Point**: \( (-1, -6) \)
- This point is not on the side since \( y = -6 \) is not in the range of \( y = -3 \) and \( y = 1 \).
4. **Point**: \( (4, -9) \)
- This point is not on the side since \( x = 4 \) is also not in the range of \( x = -8 \) and \( x = -4 \).
None of the points listed are on the sides of the square \( RSTU \). Is there any mistake in the provided options, or would more information be helpful?
The sides of the square are as follows:
1. From \( R(-8, 1) \) to \( S(-4, 1) \): This side is horizontal at \( y = 1 \) between \( x = -8 \) and \( x = -4 \).
2. From \( S(-4, 1) \) to \( T(-4, -3) \): This side is vertical at \( x = -4 \) between \( y = 1 \) and \( y = -3 \).
3. From \( T(-4, -3) \) to \( U(-8, -3) \): This side is horizontal at \( y = -3 \) between \( x = -4 \) and \( x = -8 \).
4. From \( U(-8, -3) \) to \( R(-8, 1) \): This side is vertical at \( x = -8 \) between \( y = -3 \) and \( y = 1 \).
Now, we need to check the possible coordinates given in the options to see which point lies on one of these sides:
1. **Point**: \( (-5, -3) \)
- This point is not on the side since \( x = -5 \) is not in the range of \( x = -8 \) and \( x = -4 \) for \( y = -3 \).
2. **Point**: \( (3, -3) \)
- This point is also not on the side since \( x = 3 \) is not in the range of \( x = -8 \) and \( x = -4 \) for \( y = -3 \).
3. **Point**: \( (-1, -6) \)
- This point is not on the side since \( y = -6 \) is not in the range of \( y = -3 \) and \( y = 1 \).
4. **Point**: \( (4, -9) \)
- This point is not on the side since \( x = 4 \) is also not in the range of \( x = -8 \) and \( x = -4 \).
None of the points listed are on the sides of the square \( RSTU \). Is there any mistake in the provided options, or would more information be helpful?