To rotate a point 180 degrees counterclockwise about the origin, you can simply change the signs of both the x and y coordinates of the point. For example, if the original point is (x, y), after the rotation, the new coordinates will be (-x, -y). This effectively reflects the point across the origin.
A 270-degree counterclockwise rotation around the origin in a Cartesian coordinate system transforms a point ((x, y)) to the new coordinates ((y, -x)). This means the x-coordinate becomes the y-coordinate, and the y-coordinate changes its sign and becomes the new x-coordinate. Essentially, it rotates the point three-quarters of the way around the origin.
To find the image of the point (1, -6) after a 270-degree counterclockwise rotation about the origin, we can use the rotation formula. A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation. The coordinates transform as follows: (x, y) becomes (y, -x). Therefore, the image of (1, -6) is (-6, -1).
Latin.
To find the image of the point (1, -6) after a 180-degree counterclockwise rotation about the origin, you can use the rotation transformation. A 180-degree rotation changes the coordinates (x, y) to (-x, -y). Therefore, the image of the point (1, -6) is (-1, 6).
If B was (x, y) then B' is (-y, x).
To rotate a point 180 degrees counterclockwise about the origin, you can simply change the signs of both the x and y coordinates of the point. For example, if the original point is (x, y), after the rotation, the new coordinates will be (-x, -y). This effectively reflects the point across the origin.
A 270-degree counterclockwise rotation around the origin in a Cartesian coordinate system transforms a point ((x, y)) to the new coordinates ((y, -x)). This means the x-coordinate becomes the y-coordinate, and the y-coordinate changes its sign and becomes the new x-coordinate. Essentially, it rotates the point three-quarters of the way around the origin.
To find the image of the point (1, -6) after a 270-degree counterclockwise rotation about the origin, we can use the rotation formula. A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation. The coordinates transform as follows: (x, y) becomes (y, -x). Therefore, the image of (1, -6) is (-6, -1).
Latin.
To find the image of the point (1, -6) after a 180-degree counterclockwise rotation about the origin, you can use the rotation transformation. A 180-degree rotation changes the coordinates (x, y) to (-x, -y). Therefore, the image of the point (1, -6) is (-1, 6).
A rotation of 180 degrees counterclockwise refers to turning a point or shape around a central point (such as the origin in a coordinate plane) by half a turn. This effectively moves each point to a position that is directly opposite its starting point. For example, if a point is at coordinates (x, y), after a 180-degree counterclockwise rotation, its new coordinates will be (-x, -y). This transformation maintains the shape and size but changes its orientation.
the origin and it has the coordinates of (0,0)
Origin is at points (0, 0) in coordinate geometry. If you are shifting/translating the origin, you have to add the respective x and y coordinates of the new origin with respect to the old origin to get the coordinates of the new origin.
A 180° rotation is half a rotation and it doesn't matter if it is clockwise of counter clockwise. When rotating 180° about the origin, the x-coordinate and y-coordinates change sign Thus (1, -6) → (-1, 6) after rotating 180° around the origin.
A rotation of 90 degrees counterclockwise is a transformation that turns a point or shape around a fixed point (usually the origin in a coordinate plane) by a quarter turn in the opposite direction of the clock's hands. For a point with coordinates (x, y), this rotation results in new coordinates (-y, x). This type of rotation is commonly used in geometry and computer graphics to manipulate shapes and objects.
(0,0)