To rotate a point $(-4, 1)$ 270 degrees counterclockwise around the origin, we can use the standard rotation formulas.

Rotation Formulas

When rotating a point $(x, y)$ counterclockwise about the origin:

1. 90 degrees: $(x, y) \to (-y, x)$
2. 180 degrees: $(x, y) \to (-x, -y)$
3. 270 degrees: $(x, y) \to (y, -x)$

Applying the 270-Degree Rotation

Given the point $(-4, 1)$, we use the 270-degree formula:

$(x, y) \to (y, -x)$

Substitute $(x, y) = (-4, 1)$:

$(-4, 1) \to (1, -(-4))$

Simplifying further:

$(-4, 1) \to (1, 4)$

Result

After rotating the point $(-4, 1)$ 270 degrees counterclockwise, the new coordinates are (1, 4).

Would you like to explore more on rotations or ask something else?

Follow-Up Questions:

1. What is the result of rotating the point (3, -2) by 90 degrees counterclockwise?
2. How do you rotate a point by 180 degrees around a different point than the origin?
3. What is the formula for rotating a point clockwise by 270 degrees?
4. How would you find the coordinates of a point after rotating it 45 degrees?
5. What happens if you rotate a point (x, y) by 360 degrees?

Tip: For clockwise rotations, use the counterclockwise formulas with negative angles or adjust accordingly!