The coordinates of the vertices of the image after a dilation with a scale factor of 1.5, centered at E, are D'(3, -2), E'(4, -2), F'(1.5, -3).
Dilation is a geometric transformation that involves scaling an object by a certain factor from a fixed center point. In this case, the set of triangle vertices D(2, -2), E(4, -2), and F(1, -4) undergoes a dilation with a scale factor of 1.5, centered at the point E(4, -2).
To find the coordinates of the image vertices after dilation, each vertex is multiplied by the scale factor from the center of dilation E. The new coordinates are calculated as follows:
D' (3, -2): The x-coordinate of D is multiplied by 1.5 and added to the x-coordinate of E, while the y-coordinate remains unchanged.
E' (4, -2): As the center of dilation, the coordinates of E remain the same.
F' (1.5, -3): The x-coordinate of F is multiplied by 1.5 and added to the x-coordinate of E, and the y-coordinate of F is multiplied by 1.5 and added to the y-coordinate of E.