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Use the image to answer the question.

Rectangle upper W (-2,5) upper A (8,5) upper R (8,-1) upper D (-2,-1) is plotted on a coordinate plane.

Examine the polygon in the figure shown. Identify a line of symmetry that will flip the figure onto itself.

(1 point)
Responses which answer is the correct perfect one and why

y=3
y equals 3

x=3
x equals 3

x-axis
x -axis

y-axis
y -axis

1 answer

To find a line of symmetry for the rectangle WARD with vertices at W(-2,5), A(8,5), R(8,-1), and D(-2,-1), we should observe the positions of the vertices relative to the coordinate axes.

  1. Horizontal Lines of Symmetry:

    • The rectangle is horizontal, so we can consider horizontal lines like the line \(y = 3\). This line lies exactly in the middle of the top (y = 5) and bottom (y = -1) edges of the rectangle, making it a potential line of symmetry.

  2. Vertical Lines of Symmetry:

    • We could also check the vertical line \(x = 3\). The leftmost vertex is at \(x = -2\) and the rightmost at \(x = 8\). The midpoint in the x-direction is \(x = 3\), also making it a line of symmetry.

  3. Other Axes:

    • The \(x\)-axis is not a line of symmetry since the top side (y = 5) does not reflect downwards into the bottom side (y = -1).
    • The \(y\)-axis is not a line of symmetry as well since the left side (x = -2) does not reflect to the right side (x = 8).

From the analysis:

  • Correct Answers: Both \(y = 3\) and \(x = 3\) are lines of symmetry for the rectangle. However, if you are asked for a single line, either response could be considered as correct, depending on the context requested.

If a single choice must be provided: y = 3 is a perfect answer because it divides the rectangle symmetrically horizontally, clearly matching the top and bottom sides of the rectangle.