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Question

A horizontal line separates 2 triangles. The triangle above the line is made up of points upper X (-3,9), upper Y (-2,4), and upper Z (3,4), while the triangle below the line is made up of points upper X prime, upper Y prime, and upper Z prime (3,-2)

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 which is the true correct perfect answer and tell me why by solving it

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

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

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

(−2,−2)
left parenthesis negative 2 comma negative 2 right parenthesis
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Answer 1

To find the coordinates of vertex \( X' \) after reflecting vertex \( X \) over a horizontal line of reflection, we first need to identify the initial coordinates of vertex \( X \) and the horizontal line of reflection.

1. Initial Coordinates: The coordinates for vertex \( X \) are given as \( (-3, 9) \).

2. Identify the Horizontal Line: The vertices of triangle \( XYZ \) are:

   • \( X (-3, 9) \)
   • \( Y (-2, 4) \)
   • \( Z (3, 4) \)

   To find the line of reflection, we observe that the horizontal line reflects vertices vertically. Since triangle \( XYZ \) is at a height of \( 9 \) (for vertex \( X \)) and reflects to a point below, we need to determine the y-coordinate of the horizontal line based on the midpoint of the original and reflected points.

   From point \( X \) at \( ( -3, 9 ) \) to \( X' \), we set:

   • \( y' \) (the y-coordinate of \( X' \)) should equal the negative y-coordinate of \( X \) for the reflection.

   Thus, the y-coordinate of point \( X' \) is \( -9 \).

3. Final Coordinates for X': The x-coordinate remains unchanged during a horizontal reflection, which means:

   • The x-coordinate of \( X' \) is still \(-3\), and the y-coordinate of \( X' \) after reflection is \(-9\).

Therefore, the coordinates of vertex \( X' \) are: \[ (-3, -9) \]

The correct answer is: (−3,−9)

This is because the reflection flips the y-coordinate from \( 9 \) to \( -9 \) while preserving the x-coordinate at \( -3 \).