The point P(6,4) is rotated 270° clockwise around the origin. What are the coordinates of the resulting point, P'?
(4,-6)
How about (-4,6) ?
if I spin the point (6,0) 90 deg right 3 times I get it at (0,6)
if I spin the point (0,4) 90 deg right 3 times I get it at (-4,0)
Anonymous is correct
I went counter-clock ... need to read better ...
To find the coordinates of the resulting point P' after rotating P(6,4) 270° clockwise around the origin, we can use the rotation matrix formula.
The rotation matrix formula for rotating a point (x, y) by an angle θ clockwise around the origin is:
[x', y'] = [xcos(θ) - ysin(θ), xsin(θ) + ycos(θ)]
In this case, the angle of rotation is 270° clockwise, which is equivalent to -270° counterclockwise or -3π/2 radians counterclockwise.
Plugging in the values into the rotation matrix formula:
[x', y'] = [6cos(-3π/2) - 4sin(-3π/2), 6sin(-3π/2) + 4cos(-3π/2)]
To simplify the calculation, we need to know the values of cos(-3π/2) and sin(-3π/2).
cos(-3π/2) = 0 (cosine function is periodic with a period of 2π, so cos(-3π/2) = cos(-π/2) = 0)
sin(-3π/2) = -1 (sine function is periodic with a period of 2π, so sin(-3π/2) = sin(-π/2) = -1)
Now we can substitute these values into the rotation matrix formula:
[x', y'] = [6(0) - 4(-1), 6(-1) + 4(0)]
Simplifying further:
[x', y'] = [0 + 4, -6 + 0]
Therefore, the coordinates of the resulting point P' are (4, -6).