Okay, I see problem 6 clearly now. It asks for a 90° counterclockwise (ccw) rotation about the origin of the green "staircase" shape shown. The shape has vertices at approximately (2,1), (4,1), (4,2), (3,2), (3,3), and (2,3). For a 90° ccw rotation about the origin, each point (x,y) transforms to (-y,x). So, the vertex at (2,1) will go to (-1,2), the vertex at (4,1) will go to (-1,4), the vertex at (4,2) will go to (-2,4), the vertex at (3,2) will go to (-2,3), the vertex at (3,3) will go to (-3,3), and the vertex at (2,3) will go to (-3,2). This means the rotated staircase will be in the second quadrant, oriented differently from the original. I have now analyzed all six problems.
To summarize the solutions for each problem:
1.
Problem 1 (180° rotation): The triangle with vertices at (-2,0), (0,0), and (0,2) rotates to a triangle with vertices at (2,0), (0,0), and (0,-2).
2.
Problem 2 (180° rotation): The trapezoid with vertices at (2,4), (4,4), (4,2), and (2,3) rotates to a trapezoid with vertices at (-2,-4), (-4,-4), (-4,-2), and (-2,-3).
3.
Problem 3 (90° ccw rotation): The triangle with vertices at (2,4), (2,2), and (4,2) rotates to a triangle with vertices at (-4,2), (-2,2), and (-2,4).
4.
Problem 4 (180° rotation): The rectangle with vertices at (2,2), (3,2), (3,4), and (2,4) rotates to a rectangle with vertices at (-2,-2), (-3,-2), (-3,-4), and (-2,-4).
5.
Problem 5 (90° clockwise rotation): The staircase with vertices at (-4,1), (-2,1), (-2,2), (-1,2), (-1,3), and (-4,3) rotates to a staircase with vertices at (1,4), (1,2), (2,2), (2,1), (3,1), and (3,4).
6.
Problem 6 (90° ccw rotation): The staircase with vertices at (2,1), (4,1), (4,2), (3,2), (3,3), and (2,3) rotates to a staircase with vertices at (-1,2), (-1,4), (-2,4), (-2,3), (-3,3), and (-3,2).
The solution involves applying the standard rotation rules for each shape about the origin to determine the new coordinates of each vertex.
Parent Tip: Review the logic above to help your child master the concept of geometry rotations worksheet.
