What is the new point when you rotate a geometric figure with point (5,8) 270 degrees counterclockwise about the orgin

Answer 1

To find the new point when you rotate a geometric figure with point (5,8) 270 degrees counterclockwise about the origin, we can use the rotation formula:

x' = x*cos(theta) - y*sin(theta)
y' = x*sin(theta) + y*cos(theta)

Here, x and y represent the original coordinates, and x' and y' represent the new coordinates after rotation. For a 270 degrees counterclockwise rotation, theta is equal to 270 degrees or (3/2)π radians.

Plugging in the values:

x' = 5*cos((3/2)π) - 8*sin((3/2)π)
y' = 5*sin((3/2)π) + 8*cos((3/2)π)

Using the trigonometric identities cos((3/2)π) = 0 and sin((3/2)π) = -1, we can simplify further:

x' = 5*0 - 8*(-1) = 8
y' = 5*(-1) + 8*0 = -5

Therefore, the new point after rotating (5,8) 270 degrees counterclockwise about the origin is (8, -5).