What is the image of the point (1,-9) after a rotation of 180° counterclockwise about the origin?
(-1,9)
Nooo it (1,9)
okay, Anonymous ... draw the picture and try it
Both are wrong, the answer is (-4,-9).
To find the image of a point after a rotation, we need to know the coordinates of the point and also the angle and direction of rotation.
In this case, the point is (1,-9), and we want to rotate it 180° counterclockwise about the origin.
To perform a counterclockwise rotation of 180° about the origin, we can follow these steps:
1. Multiply the coordinates of the original point by the rotation matrix:
[ cos(180°) -sin(180°) ]
[ sin(180°) cos(180°) ]
Since cos(180°) = -1 and sin(180°) = 0, the rotation matrix becomes:
[ -1 0 ]
[ 0 -1 ]
Multiplying the rotation matrix by the coordinates of the original point (1,-9), we get:
[ -1*1 + 0*(-9) ]
[ 0*1 + (-1)*(-9) ]
Simplifying the multiplication, we have:
[ -1 ]
[ 9 ]
So the image of the point (1,-9) after the rotation of 180° counterclockwise about the origin is (-1,9).