Given a point on a geometric figure (x, y) , what is the new point when the figure is rotated clockwise about the origin 270 degrees?
To find the new point when the figure is rotated clockwise about the origin 270 degrees, we can use the following rotation matrix:
|cos(theta) -sin(theta)|
|sin(theta) cos(theta)|
In this case, theta = -270 degrees.
|cos(-270°) -sin(-270°)|
|sin(-270°) cos(-270°)|
We know that cos(-270°) = 0 and sin(-270°) = -1.
| 0 1|
|-1 0|
Multiplying the original point (x, y) by this rotation matrix will give us the new point after the rotation:
| 0 1| |x| |y|
|-1 0| * |y| = |-x|
Therefore, the new point after rotating the figure clockwise about the origin 270 degrees is (-y, x).
different then (-y, x)
Apologies for the mistake in my previous response. Let's correct it.
To find the new point when the figure is rotated clockwise about the origin 270 degrees, we can use the following transformation:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
In this case, theta = -270 degrees.
x' = x * cos(-270°) - y * sin(-270°)
y' = x * sin(-270°) + y * cos(-270°)
We know that cos(-270°) = 0 and sin(-270°) = -1.
x' = x * 0 - y * (-1)
y' = x * (-1) + y * 0
Simplifying further:
x' = y
y' = -x
Therefore, the new point after rotating the figure clockwise about the origin 270 degrees is (y, -x).