\( \triangle A B C \) is dilated about the origin, resulting in \( \triangle X Y Z \). Point \( Z \) is located at \( (72,0) \). What are the coordinates of point \( X \) ? The coordinates of point \( X \) are (Type an ordered pair.)

To find the coordinates of point \( X \) in triangle \( \triangle A B C \), we need to consider the dilation that occurred about the origin to get to triangle \( \triangle X Y Z \). Knowing that point \( Z \) is at \( (72,0) \), we can assume there is a constant scale factor \( k \). If point \( Z \) corresponds to point \( C \) in the original triangle \( \triangle ABC \) and has coordinates \( (c_x, c_y) \), the coordinates after dilation can be expressed as: \[ Z = (k \cdot c_x, k \cdot c_y) \] Given \( Z = (72, 0) \), we can set \( k \cdot c_x = 72 \) and \( k \cdot c_y = 0 \). This means \( c_y \) must be 0, indicating that point \( C \) was also on the x-axis. Assuming the same scale factor applies for points \( A \) and \( B \) to form \( X \) and \( Y \), the coordinates of point \( X \) will be computed similarly using the scale factor relative to point \( A \) at \( (a_x, a_y) \): \[ X = (k \cdot a_x, k \cdot a_y) \] Without information on the original coordinates of \( A \), we cannot calculate a specific value for \( X \). If you have specific coordinates for points \( A \) and \( B \), please provide them, and then we can derive point \( X \)'s coordinates together. However, if you assume point \( A \) also went through the same dilation process, and if \( X \) corresponds to point \( A \) with coordinates proportional to \( (k \cdot a_x, k \cdot a_y) \), you can use known coordinates for \( c \) to share a consistent scale factor. Are there any other details we can dig in together to find point \( X \)?