Use the image to answer the question.

Question

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

(3, −7)
open paren 3 comma space negative 7 close paren

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

(−3, −8)

Answer 1

To find the coordinates of vertex \( X' \) after reflecting vertex \( X(-3, 8) \) over the line \( y = 1 \), we first need to calculate the distance from the vertex \( X \) to the line of reflection.

1. The line of reflection is \( y = 1 \).
2. The y-coordinate of point \( X \) is \( 8 \).
3. The distance from \( X \) to the line \( y = 1 \) is: \[ 8 - 1 = 7 \]
4. To find the reflected point \( X' \), we move the same distance downward from the line of reflection: \[ 1 - 7 = -6 \]

So, the coordinates of vertex \( X' \) after the reflection are \( (-3, -6) \).

The answer is: (−3, −6)