when you're rotating a trapezoid that's in quadrant 4 90 degrees, does the trapezoid goes in quadrant 2 and the coordiantes switch?
also, does the trapezoid goes in quadrant 1 when rotating 180 degrees?
no one's answering.
It depends on which way the rotation is. Normally, we rotate to the counter clockwise direction, so quadrant 4 goes to quadrant 1. If you rotate clockwise, it goes to quadrant 2.
Quadrant 4 to 180 degrees is in quadrant 2.
To rotate a trapezoid 90 degrees counterclockwise in quadrant 4, you can follow these steps:
1. Identify the coordinates of the trapezoid's vertices in quadrant 4. Let's say the vertices are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4).
2. To rotate the trapezoid 90 degrees counterclockwise, you need to swap the x and y coordinates of each vertex and change their signs.
- The new coordinates of vertex A will be A'(-y1, x1).
- The new coordinates of vertex B will be B'(-y2, x2).
- The new coordinates of vertex C will be C'(-y3, x3).
- The new coordinates of vertex D will be D'(-y4, x4).
3. After performing the coordinate transformations, the trapezoid will indeed move to quadrant 2, and the coordinates will switch as described above.
Now, to rotate the trapezoid 180 degrees counterclockwise, you can follow these steps:
1. Once again, identify the coordinates of the trapezoid's vertices.
2. To rotate the trapezoid 180 degrees counterclockwise, you need to negate both the x and y coordinates of each vertex.
- The new coordinates of vertex A will be A'(-x1, -y1).
- The new coordinates of vertex B will be B'(-x2, -y2).
- The new coordinates of vertex C will be C'(-x3, -y3).
- The new coordinates of vertex D will be D'(-x4, -y4).
After performing the coordinate transformations, the trapezoid will move to quadrant 1.
Remember, when rotating counterclockwise, the trapezoid moves as mentioned above. However, if you rotate clockwise, the trapezoid will move to different quadrants following different coordinate transformations.