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A) The triangles are reflected across the x-axis.

B) The triangles are reflected across the y-axis.
C) The triangles are reflected across the line y = x.
D) The triangles are reflected across the line y = -x.

User Davidgoli
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1 Answer

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Final Answer:

The triangles are reflected across the line y = -x.

Step-by-step explanation:

In geometry, a reflection involves flipping an object over a line. In this case, the line of reflection is y = -x. When a shape is reflected across the line y = -x, each point in the original shape is transformed to a new point equidistant on the opposite side of the line. The line y = -x bisects the angle formed by the x-axis and y-axis at a 45-degree angle, meaning it reflects points across a diagonal axis.

The reflection across y = -x swaps the x and y coordinates of each point, effectively mirroring the shape in a manner that retains the same size and orientation. This transformation is distinct from reflections across the x-axis, y-axis, or the line y = x. Reflections across the x-axis invert the y-coordinates, while reflections across the y-axis invert the x-coordinates.

The line y = x swaps the x and y coordinates but also changes the orientation by a 90-degree angle. The correct choice, y = -x, ensures that the triangles are flipped across a diagonal axis with an interchange of x and y coordinates while preserving the shape's overall structure.

User Lee Buckle
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