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?(1 point)
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To find the new coordinates after rotating a point (x, y) clockwise 270 degrees about the origin, we can use the following formula:
New x-coordinate = x * cos(angle) + y * sin(angle)
New y-coordinate = -x * sin(angle) + y * cos(angle)
In this case, the angle is 270 degrees, which is equal to -90 degrees in standard position. Therefore, we can substitute -90 degrees into the formula:
New x-coordinate = x * cos(-90) + y * sin(-90)
New y-coordinate = -x * sin(-90) + y * cos(-90)
Using the trigonometric identities cos(-90) = 0 and sin(-90) = -1, we can simplify the formula:
New x-coordinate = x * 0 + y * (-1) = -y
New y-coordinate = -x * (-1) + y * 0 = x
Therefore, the new point after rotating (x, y) clockwise 270 degrees about the origin is (-y, x).