Question
There is a rectangle on a grid with the corners coordinates being A(8,5) R(8,-1), D(-2,-1), W(-2,-5)
Examine the polygon in the figure shown. Identify a line of symmetry that will flip the figure onto itself.
A. x-axis
B. x=3
C. y-axis
D. y=3
Examine the polygon in the figure shown. Identify a line of symmetry that will flip the figure onto itself.
A. x-axis
B. x=3
C. y-axis
D. y=3
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine if there is a line of symmetry for the rectangle formed by the points A(8,5), R(8,-1), D(-2,-1), and W(-2,-5), let's first analyze the coordinates of the rectangle.
1. The points A(8,5) and R(8,-1) are vertically aligned (same x-coordinate).
2. The points D(-2,-1) and W(-2,-5) are also vertically aligned.
3. The rectangle can be confirmed since opposite sides are parallel and equal in length.
To find a line of symmetry, we need to see if the rectangle can be folded over a line and result in both sides matching perfectly.
- **x-axis**: This line would reflect points A and R (top edge) to below the x-axis, and D and W (bottom edge) to above the x-axis, which does not maintain symmetry. So **not a line of symmetry**.
- **x = 3**: This line is positioned between the left and right edges of the rectangle (from x = -2 to x = 8). Reflecting points across x = 3 would not put them in their original positions since the distances from that line are unequal. So **not a line of symmetry**.
- **y-axis**: The points at A and R would reflect to (8,5) and (8,-1) on the opposite side of the y-axis, and D and W would change to (-2,-1) and (-2,-5) which do not match their original locations. So **not a line of symmetry**.
- **y = 3**: This line runs through the midpoint of the vertical height of the rectangle. The top edge (points A, R) would reflect down to points D and W respectively. Since the rectangle maintains a consistent distance from this line on both sides, it creates a perfect match.
Thus, the line of symmetry identified is:
**D. y = 3**
1. The points A(8,5) and R(8,-1) are vertically aligned (same x-coordinate).
2. The points D(-2,-1) and W(-2,-5) are also vertically aligned.
3. The rectangle can be confirmed since opposite sides are parallel and equal in length.
To find a line of symmetry, we need to see if the rectangle can be folded over a line and result in both sides matching perfectly.
- **x-axis**: This line would reflect points A and R (top edge) to below the x-axis, and D and W (bottom edge) to above the x-axis, which does not maintain symmetry. So **not a line of symmetry**.
- **x = 3**: This line is positioned between the left and right edges of the rectangle (from x = -2 to x = 8). Reflecting points across x = 3 would not put them in their original positions since the distances from that line are unequal. So **not a line of symmetry**.
- **y-axis**: The points at A and R would reflect to (8,5) and (8,-1) on the opposite side of the y-axis, and D and W would change to (-2,-1) and (-2,-5) which do not match their original locations. So **not a line of symmetry**.
- **y = 3**: This line runs through the midpoint of the vertical height of the rectangle. The top edge (points A, R) would reflect down to points D and W respectively. Since the rectangle maintains a consistent distance from this line on both sides, it creates a perfect match.
Thus, the line of symmetry identified is:
**D. y = 3**
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.