Question

What are the coordinate points of A’ (1,7) if A undergoes a rotation of

90 degrees clockwise
180 degrees clockwise
279 degrees clockwise

Answer 1

To find the coordinates of A' after a rotation, we can use the rotational formulas.

1) 90 degrees clockwise rotation:
To rotate a point (x, y) 90 degrees clockwise, we swap the coordinates and negate the new x-coordinate.
So, A' in this case would be (y, -x) = (7, -1).

2) 180 degrees clockwise rotation:
To rotate a point (x, y) 180 degrees clockwise, we negate both coordinates.
So, A' in this case would be (-x, -y) = (-1, -7).

3) 279 degrees clockwise rotation:
A 279 degrees clockwise rotation is equivalent to a 81 degrees counterclockwise rotation.
To find A' in this case, we can use the formula for counterclockwise rotation:
A' = (x*cosθ - y*sinθ, x*sinθ + y*cosθ),
where θ is the angle in radians (1 radian ≈ 57.3 degrees).

Using this formula, we have:
θ = 81 degrees ≈ 1.41 radians (rounded to two decimal places)
x = 1, y = 7
A' = (1*cos1.41 - 7*sin1.41, 1*sin1.41 + 7*cos1.41)
A' ≈ (-5.58, -4.01) (rounded to two decimal places)