4. Polygon ABCDEF is translated up 1 unit and to the right 4 units, rotated 90°, and then reflected across the line y=x to produce the image polygon A′B′C′D′E′F′. What are the coordinates of E′?
A. (6,1)
B. (9,−1)
C. (1,0)
D. (4,−4)
First, we need to find the coordinates of each vertex after each transformation:
- Translated up 1 unit and to the right 4 units:
A (0,0) → A' (4,1)
B (2,0) → B' (6,1)
C (3,2) → C' (7,3)
D (3,4) → D' (7,5)
E (1,4) → E' (5,5)
F (0,2) → F' (4,3)
- Rotated 90° clockwise:
A' (4,1) → A'' (1,-4)
B' (6,1) → B'' (1,-6)
C' (7,3) → C'' (3,-7)
D' (7,5) → D'' (5,-7)
E' (5,5) → E'' (5,-5)
F' (4,3) → F'' (3,-4)
- Reflected across the line y=x:
A'' (1,-4) → A''' (-4,1)
B'' (1,-6) → B''' (-6,1)
C'' (3,-7) → C''' (-7,3)
D'' (5,-7) → D''' (-7,5)
E'' (5,-5) → E''' (-5,5)
F'' (3,-4) → F''' (-4,3)
Therefore, the coordinates of E' are (5,-5), and the answer is choice E.