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A triangle is shown. Drag graphs to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, or the line y = x.
Reflected Over:
x-axis
y-axis
y = x
Graph
DRAG AND DROP AN ITEM HERE
DRAG AND DROP AN ITEM HERE
DRAG AND DROP AN ITEM HERE
To analyze the reflection of a triangle over different axes, let’s discuss how each reflection works.
1. Reflection over the x-axis: When a point ((x, y)) is reflected over the x-axis, the new point becomes ((x, -y)). This means the y-coordinate changes sign while the x-coordinate remains the same.
2. Reflection over the y-axis: For a point ((x, y)) reflected over the y-axis, the new point is ((-x, y)). Here, the x-coordinate changes sign, but the y-coordinate stays the same.
3. Reflection over the line y = x: In this case, a point ((x, y)) becomes ((y, x)). Both coordinates switch places.
To proceed, identify the coordinates of the vertices of the triangle from the image. Then apply the transformations based on the reflections described above to find the new coordinates and match them with the correct graphs in the table.
If you have specific coordinates or graphs to work with, feel free to share, and I can guide you through the calculations!