Question

What is the result of rotating the quadrilateral with vertices A(-5,5), B(-6,2), C(-5,1), D(2,2) by 180 degrees?

1) A(-5,-5), B(-6,-2), C(-5,-1), D(2,-2)
2) A(5,-5), B(6,-2), C(5,-1), D(-2,-2)
3) A(5,5), B(6,2), C(5,1), D(-2,2)
4) A(-5,-5), B(-6,-2), C(-5,-1), D(-2,-2)

Answer 1

After rotating the given quadrilateral 180 degrees, the vertices A, B, C, and D have their sign reversed for both coordinates, leading to the new positions A(5,-5), B(6,-2), C(5,-1), D(-2,-2), which corresponds to option 2.

Step-by-step explanation:

To find the result of rotating a quadrilateral 180 degrees about the origin, you reverse the sign of both the x and y coordinates for each vertex. This is equivalent to reflecting the quadrilateral over both axes. Using the given vertices A(-5,5), B(-6,2), C(-5,1), and D(2,2), we can calculate the new positions post-rotation.

• A' = A(-5,5) becomes A'(5,-5)
• B' = B(-6,2) becomes B'(6,-2)
• C' = C(-5,1) becomes C'(5,-1)
• D' = D(2,2) becomes D'(-2,-2)

Therefore, the correct answer is option 2, which is A(5,-5), B(6,-2), C(5,-1), D(-2,-2).