To find the coordinates of point B after a 270° rotation about the origin, we can use the rotation transformation rules.
The general rule for rotating a point \((x, y)\) counterclockwise by 270° (which is the same as a clockwise rotation of 90°) about the origin is given by: \[ (x, y) \rightarrow (y, -x) \]
If we denote the original point \(B\) as \((x, y)\), after applying the transformation for a 270° rotation:
- Let \(B\) be at coordinates \((x, y)\).
- After the rotation, the new coordinates will be \((y, -x)\).
Now, without knowing the exact coordinates of point B, we cannot calculate the result directly. However, let's consider each of the answer choices provided and see how to reach them:
- If \(B = (4, 2)\):
- After rotation: \((2, -4)\)
- If \(B = (2, 4)\):
- After rotation: \((4, -2)\)
- If \(B = (-4, -2)\):
- After rotation: \((-2, 4)\)
- If \(B = (-2, -4)\):
- After rotation: \((-4, 2)\)
Among the options provided:
- \((4, 2)\) rotates to \((2, -4)\)
- \((2, 4)\) rotates to \((4, -2)\)
- \((-4, -2)\) rotates to \((-2, 4)\)
- \((-2, -4)\) rotates to \((-4, 2)\)
It's important to determine the starting coordinates of point B. If you check the coordinates of B directly from your graph, you can apply the rotations above accordingly.
Please provide the coordinates of point B, and I can give the exact answer based on the rotation.