Given a point (9,−3) on a geometric figure, what is the new point when the figure is rotated counterclockwise about the origin 180 degrees?(1 point)
When a point is rotated counterclockwise about the origin by 180 degrees, the coordinates are switched in sign.
So, if the original point is (9, -3), when rotated counterclockwise about the origin by 180 degrees, the new point would be (-9, 3).
To find the new point after rotating (9, -3) counterclockwise about the origin 180 degrees, we can use the following steps:
1. When rotating a point counterclockwise about the origin, we can use the rotation formula:
- x' = x * cos(theta) - y * sin(theta)
- y' = x * sin(theta) + y * cos(theta)
2. Since we want to rotate the point (9, -3) 180 degrees counterclockwise, we can substitute theta = 180 degrees into the equations:
x' = 9 * cos(180) - (-3) * sin(180)
y' = 9 * sin(180) + (-3) * cos(180)
3. Evaluating the trigonometric functions at 180 degrees:
- cos(180) = -1
- sin(180) = 0
4. Substituting the values:
x' = 9 * (-1) - (-3) * 0
y' = 9 * 0 + (-3) * (-1)
5. Simplifying the calculations:
x' = -9
y' = 3
Therefore, the new point after rotating (9, -3) counterclockwise about the origin 180 degrees is (-9, 3).