Question

" Pentagon ABCDE and pentagon A’B’C’D’E’ are shown on the coordinate plane below.

Which two transformations are applied to pentagon ABCDE to create A’B’C’D’E’?
a. translated according to the rule (x, y) → (x + 2, y + 8) and reflected across the x-axis
b. translated according to the rule (x, y) → (x + 8, y + 2) and reflected across the x-axis
c. translated according to the rule (x, y) → (x + 2, y + 8) and reflected across the y-axis
d. translated according to the rule (x, y) → (x + 8, y + 2) and reflected across the y-axis

"

Answer 1

C. translated according to the rule (x,y) > (x+2,y+8) and reflected across the y-axis

Answer 2

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.