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

In dilation, the coordinates of the points are scaled by a certain factor \( k \) with respect to the origin. Given that point \( Z \) in triangle \( XYZ \) is located at \( (72, 0) \), we can consider its corresponding point \( C \) in triangle \( ABC \), which would be found by applying the same scaling factor to its coordinates. For example, if the dilation factor \( k \) is known, we can write the coordinates of point \( C \) as \( (x, y) \). Then, point \( Z \)'s coordinates can be expressed as \( (k \cdot x, k \cdot y) = (72, 0) \). To find the coordinates of point \( Z \), we need to find point \( X \) by applying the same scale factor on point \( A \) of triangle \( ABC \). Without loss of generality, if we assume triangle \( ABC \) has point \( A \) at \( (a_1, b_1) \), then point \( X \) would have coordinates \( (k \cdot a_1, k \cdot b_1) \). To directly find point \( X \), additional information like the coordinates of triangle \( ABC \) or the dilation factor \( k \) is required. Without this, we can't determine the exact coordinates of point \( X \) purely from the information given.