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Triangle upper X upper Y upper Z on the coordinate plane above a line of reflection.



Image Long DescriptionThe horizontal axis ranges from negative 5 to 5. The vertical axis ranges from negative 1 to 9. Triangle upper X upper Y upper Z has vertices as follows upper X negative 3 comma 8, upper Y negative 2 comma 4, and upper Z 3 comma 4. The horizontal line of reflection is y equals 1.

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, −6)
open paren negative 3 comma space negative 6 close paren

(−2, −2)
open paren negative 2 comma space negative 2 close paren

(−3, −8)
open paren negative 3 comma space negative 8 close paren

(3, −7)

1 answer

To find the coordinates of vertex \( X' \) after reflecting triangle \( XYZ \) over the line \( y = 1 \), we start with the coordinates of vertex \( X \), which are \( (-3, 8) \).

  1. Determine the distance from vertex \( X \) to the line of reflection \( y = 1 \):

    • The y-coordinate of \( X \) is \( 8 \).
    • The distance from \( 8 \) to \( 1 \) is \( 8 - 1 = 7 \) units.

  2. Since reflection over the line means moving the same distance to the opposite side:

    • We subtract the distance from \( 1 \) (the line of reflection):
    • New y-coordinate after reflection: \( 1 - 7 = -6 \).

  3. The x-coordinate remains the same, so:

    • The new coordinates of vertex \( X' \) are \( (-3, -6) \).

Thus, the coordinates of vertex \( X' \) are \( \boxed{(-3, -6)} \).