The coordinates of the image of point E after the sequence of transformations are (-5, 0).
In this exercise, we would apply a translation 4 units down to the pre-image, in order to determine the coordinates of its image as follows;
(x, y) → (x, y - 4)
Point E (5, 4) → (5, 4 - 4) = Point E' (5, 0).
Furthermore, the mapping rule for the counterclockwise rotation of a geometric figure about the origin by 180° can be modeled by this mathematical expression:
(x, y) → (-x, -y)
Point E' (5, 0) → Point E" = (-5, 0)
In conclusion, we can logically deduce that the coordinates of the image of point E after translating the pre-image down 4 units and rotating 180° counterclockwise are (-5, 0).
Complete Question:
The figure below is translated down 4 units and then rotated 180° counterclockwise. What are the coordinates of the image of point E after these transformations?