what is the image of the point (-2,7) after a rotation of 180 counterclockwise about the origin?
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).
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).
To find the image of the point (4, 3) after a 90-degree rotation counterclockwise about the origin, you can use the transformation formula for rotation. The new coordinates will be (-y, x), which means the image of the point (4, 3) will be (-3, 4).
The answer will depend on whether the rotation is clockwise or counterclockwise.
The answer will depend on whether the rotation is clockwise or counterclockwise.
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.
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.
A counterclockwise rotation of 270 degrees about the origin is equivalent to a clockwise rotation of 90 degrees. To apply this transformation to a point (x, y), you can use the rule: (x, y) transforms to (y, -x). This means that the x-coordinate becomes the y-coordinate, and the y-coordinate becomes the negative of the x-coordinate.
What is the image of point (3, 5) if the rotation is
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 rotation of 270 degrees clockwise is equivalent to a rotation of 90 degrees counterclockwise. In a Cartesian coordinate system, this means that a point originally at (x, y) will move to (y, -x) after the rotation. Essentially, it shifts the point three-quarters of the way around the origin in the clockwise direction.
A rotation of 270 degrees counterclockwise is a transformation that turns a figure around a fixed point by 270 degrees in the counterclockwise direction. This rotation can be visualized as a quarter turn in the counterclockwise direction. It is equivalent to rotating the figure three-fourths of a full revolution counterclockwise.