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 (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 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.
To find the image of ABC for a 180-degree counterclockwise rotation about point P, we would reflect each point of the triangle across the line passing through P. The resulting image of ABC would be a congruent triangle with its vertices in opposite positions relative to the original triangle.
To find the image of the point (5, 4) when rotated 180 degrees about the origin, you can apply the transformation that changes the signs of both coordinates. Thus, the new coordinates will be (-5, -4). Therefore, the image of the point (5, 4) after a 180-degree rotation about the origin is (-5, -4).