Final answer:
To rotate the point (4, -1) 270 degrees counterclockwise, use the formulas: new x-coordinate = old x-coordinate * cos(theta) - old y-coordinate * sin(theta) and new y-coordinate = old x-coordinate * sin(theta) + old y-coordinate * cos(theta). Applying these formulas, the new coordinates are (-1, -4).
Step-by-step explanation:
To rotate a point counterclockwise, we need to use the following formulas:
New x-coordinate = old x-coordinate * cos(theta) - old y-coordinate * sin(theta)
New y-coordinate = old x-coordinate * sin(theta) + old y-coordinate * cos(theta)
Applying these formulas to the point (4, -1) and rotating it 270 degrees counterclockwise:
New x-coordinate = 4 * cos(270) - (-1) * sin(270) = 4 * 0 - (-1) * (-1) = -1
New y-coordinate = 4 * sin(270) + (-1) * cos(270) = 4 * (-1) + (-1) * 0 = -4
Therefore, the new coordinates of the point are (-1, -4). Option 1 is the correct answer.