On a coordinate plane, a rectangle is shown with points S (4, negative 4), R (4, negative 10), Q (negative 7, negative 10), and R (negative 7, negative 4). A dashed line is on the x-axis.

Question

What are the coordinates of the image of vertex P after a reflection of rx-axis(x, y)?

P'(
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Answer 1

To find the image of a point \( P(x, y) \) after a reflection across the x-axis, you change the y-coordinate to its opposite while keeping the x-coordinate the same.

The transformation can be described as: \[ P'(x, y) \rightarrow P'(x, -y) \]

Assuming \( P \) is one of the vertices of the rectangle S(4, -4), R(4, -10), Q(-7, -10), and R(-7, -4), let's first clarify that we likely have a naming issue with the points as R is mentioned twice.

Let's take for example the point S(4, -4). After reflecting across the x-axis:

1. Keep the same x-coordinate: \( x = 4 \)
2. Change the y-coordinate to its opposite: \( y = -4 \) becomes \( y' = 4 \)

Therefore, the coordinates of the image of point S after reflection will be \( S'(4, 4) \).

If you meant a different vertex, please replace the coordinates of point P. For example, if P is R(4, -10), then after reflection:

1. Keep the x-coordinate, so \( x = 4 \)
2. Change the y-coordinate: \( y = -10 \) becomes \( y' = 10 \)

So, the coordinates would be \( R'(4, 10) \).

Feel free to specify the exact point P if it's different from the points provided!