Question

The vertices of polygon ABCD are at A(1, 1), B(2, 3), C(3, 2), and D(2, 1). ABCD is reflected across the x-axis and translated 2 units up to form polygon A'B'C'D'. Match each vertex of polygon A'B'C'D' to its coordinates.

A' (2, 1)
B' (1, 1)
C' (3, 0)
D' (2, 3)

Answer 1

To match the vertices of the reflected and translated polygon A'B'C'D' to its coordinates, invert the y-values for reflection and then add 2 to the y-values for the translation. The correct coordinates are A'(1, 1), B'(2, -1), C'(3, 0), D'(2, 1).

Step-by-step explanation:

The question pertains to the transformation of a polygon in the coordinate plane, specifically reflection and translation. To match each vertex of polygon A'B'C'D' to its coordinates, we must apply these transformations step by step. Given the original coordinates for vertices A(1, 1), B(2, 3), C(3, 2), and D(2, 1), reflecting them across the x-axis will invert the y-coordinates, and then translating the result 2 units up will add 2 to the y-coordinates.

Reflection across the x-axis:

A' becomes (1, -1), B' becomes (2, -3), C' becomes (3, -2), D' becomes (2, -1)

Translation 2 units up:

A' becomes (1, 1), B' becomes (2, -1), C' becomes (3, 0), D' becomes (2, 1)

Therefore, the correct coordinates after these transformations are:

• 
  
• A' (1, 1)
• 
  
• B' (2, -1)
• 
  
• C' (3, 0)
• 
  
• D' (2, 1)