What are the coordinate points of A′ if A (5, 6) undergoes a rotation of: (Click Here for Help Video 1. Click Here for Help Video 2.)(10 points) 180° clockwise: 180° counterclockwise:
To find the coordinate points of A' after a rotation of 180°, we can use the following formulas for the rotation of a point (x, y) about the origin:
Rotation clockwise:
x' = x*cos(theta) + y*sin(theta)
y' = -x*sin(theta) + y*cos(theta)
Rotation counterclockwise:
x' = x*cos(theta) - y*sin(theta)
y' = x*sin(theta) + y*cos(theta)
In this case, since we are rotating 180°, we can substitute theta with pi:
Rotation clockwise:
x' = x*cos(pi) + y*sin(pi)
y' = -x*sin(pi) + y*cos(pi)
Rotation counterclockwise:
x' = x*cos(pi) - y*sin(pi)
y' = x*sin(pi) + y*cos(pi)
Let's calculate each case:
180° clockwise:
x' = 5*cos(pi) + 6*sin(pi) = -5 + 0 = -5
y' = -5*sin(pi) + 6*cos(pi) = 0 - 6 = -6
Therefore, A' has the coordinate points (-5, -6) after a rotation of 180° clockwise.
180° counterclockwise:
x' = 5*cos(pi) - 6*sin(pi) = -5 + 0 = -5
y' = 5*sin(pi) + 6*cos(pi) = 0 + 6 = 6
Therefore, A' has the coordinate points (-5, 6) after a rotation of 180° counterclockwise.