Use the image to answer the question.

Question

Triangle XYZ is reflected over a horizontal line of reflection to create triangle X′Y′Z′. What are the coordinates of vertex X′?

(1 point)
Responses

(−3,−7)
left parenthesis negative 3 comma negative 7 right parenthesis

(−3,−9)
left parenthesis negative 3 comma negative 9 right parenthesis

(−2,−2)
left parenthesis negative 2 comma negative 2 right parenthesis

(3,−9)

Answer 1

To determine the coordinates of vertex X′ after reflecting triangle XYZ over a horizontal line of reflection, we first need to understand the vertical distance of point X from the line of reflection.

When reflecting a point over a horizontal line, the x-coordinate remains the same, while the y-coordinate is transformed based on the distance from the line of reflection. If the original point has a y-coordinate above the line, the reflected point will have the same distance below the line.

Without the image or specific coordinates for vertex X (e.g. (x, y)), we cannot provide the exact answer for the coordinates of vertex X′. However, you can follow these steps:

1. Identify the coordinates of vertex X (let's say they are (x, y)).
2. Determine the y-coordinate of the horizontal line of reflection.
3. Calculate the distance from point X to the line.
4. Subtract that distance from the y-coordinate of the line to find the y-coordinate of X′.

Once we have those coordinates, we could match them with the given responses. If you have the coordinates of vertex X or the horizontal line of reflection, please provide them to find the correct answer.