Question

The point (4, -1) is rotated 270 degrees counterclockwise. What are the new coordinates of the point?

Option 1: (-1, -4)
Option 2: (-4, 1)
Option 3: (1, 4)
Option 4: (1, -4)

Answer 1

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.