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

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

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

Answer 1

To find the coordinates of vertex \(X'\) after reflecting vertex \(X(-3, 8)\) over the horizontal line of reflection \(y = 1\), we can follow these steps:

1. Identify the distance from the vertex \(X\) to the line of reflection \(y = 1\). The y-coordinate of point \(X\) is \(8\).

   • The distance from \(8\) to \(1\) is \(8 - 1 = 7\).

2. Since we are reflecting, we move the same distance below the line of reflection. Therefore, we subtract \(7\) from \(1\):

   • \(1 - 7 = -6\).

The new coordinates of vertex \(X'\) after reflection will be \((-3, -6)\).

Thus, the answer is \((−3, −6)\).