Question

The point K(-1, -4) is rotated 270° counterclockwise around the origin. What are the coordinates of the resulting point, K'?

Answer 1

To rotate a point counterclockwise around the origin, we can use the formula x' = x*cos(angle) - y*sin(angle) and y' = x*sin(angle) + y*cos(angle), where (x, y) are the coordinates of the original point and (x', y') are the coordinates of the resulting point.

Step-by-step explanation:

To rotate a point counterclockwise around the origin, we can use the formula x' = x*cos(angle) - y*sin(angle) and y' = x*sin(angle) + y*cos(angle), where (x, y) are the coordinates of the original point and (x', y') are the coordinates of the resulting point. In this case, the angle is 270°. Plugging in the values for the point K(-1, -4), we get:

x' = -1*cos(270°) - (-4)*sin(270°) = 0 - 4 = -4

y' = -1*sin(270°) + (-4)*cos(270°) = -(-1) - 4*0 = 1

Therefore, the coordinates of the resulting point K' are (-4, 1).