A trapezoid is graphed on a coordinate grid and then reflected across the x-axis. Then, the new image of the trapezoid was reflected again, but this time over the y-axis. If a vertex of the original trapezoid is located at (x, y), which ordered pair represents the new vertex after both transformations have been applied?
(x,y)→(x,-y)→(-x,-y)
To find the new vertex after both transformations have been applied, we need to understand how the reflections across the x-axis and y-axis affect the coordinates.
Reflection across the x-axis: When a point (x, y) is reflected across the x-axis, the y-coordinate changes its sign. So, the new y-coordinate becomes -y, while the x-coordinate remains the same.
Reflection across the y-axis: When a point (x, y) is reflected across the y-axis, the x-coordinate changes its sign. So, the new x-coordinate becomes -x, while the y-coordinate remains the same.
Now, let's apply these transformations step by step.
Original vertex: (x, y)
After reflection across the x-axis: (x, -y)
After reflection across the y-axis: (-x, -y)
Therefore, the ordered pair that represents the new vertex after both transformations have been applied is (-x, -y).