Pentagon ABCDE has vertices with coordinates A(-5,-2), B(-7,-3), C(-6,-6), D(-3,-5) and E(-3,-3).
1. Apply the translation (x, y) → (x + 2, y + 8) to the pentagon ABCDE. Then the coordinates of vertices of image pantagon A''B''C''D''E'' will be:
- A(-5,-2)→A''(-3,6),
- B(-7,-3)→B''(-5,5),
- C(-6,-6)→C''(-4,2),
- D(-3,-5)→D''(-1,3),
- E(-3,-3)→E''(-1,5).
2. Apply to the pentagon A''B''C''D''E'' the reflection across the y-axis that has a rule (x,y)→(-x,y). Then the coordinates of image pentagon A'B'C'D'E' will be:
- A''(-3,6)→A'(3,6),
- B''(-5,5)→B'(5,5),
- C''(-4,2)→C'(4,2),
- D''(-1,3)→D'(1,3),
- E''(-1,5)→E'(1,5).
As you can see from the diagram these obtained coordinates are exactly the same as the coordinates of drawn points.
Answer: correct choice is C.
