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A rotation of 180 degrees about the origin in a Cartesian coordinate system transforms any point ((x, y)) to ((-x, -y)). This means that the point is flipped to the opposite side of the origin, effectively reflecting it across both axes. This transformation maintains the distance from the origin but reverses the direction. As a result, the shape and size of geometric figures remain unchanged, but their positions are inverted.
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What is the rule for a counterclockwise rotation about the origin of 270?
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.
If triangle DEF is rotated 180 degrees clockwise around the origin what will be the coordinates of point E in the image D (-13) E (31) and F (2-2)?
add the
Is rotation scalar or vector?
Rotation is a vector having a direction and magnitude.
The point where x and y axis meet?
It is the origin
How you find six trig functions of 180 degree?
To find the six trigonometric functions of 180 degrees, we can use the unit circle. At 180 degrees, the coordinates of the point on the unit circle are (-1, 0). Thus, the sine function (sin) is 0, the cosine function (cos) is -1, and the tangent function (tan) is 0. Consequently, the values for the six trig functions are: sin(180°) = 0, cos(180°) = -1, tan(180°) = 0, csc(180°) is undefined, sec(180°) = -1, and cot(180°) is undefined.
What is the image of 1 -6 after a 180 degree counterclockwise rotation about the 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.
What is the image of (1 -6) for a 180 degree counterclockwise rotation 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).
what is the image of the point (-2,7) after a rotation of 180 counterclockwise about the origin?
The rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .
What is the image of (1 -6) for a 180 counterclockwise rotation about the origin?
It is (-1, 6).Also, if the rotation is 180 degrees, then clockwise or anticlockwise are irrelevant.It is (-1, 6).
What happens to the x- coordinate during a 180 degree rotation?
depends on the centre of rotation if it's about the origin the x coord is multiplied by -1
Is the composition of a reflection across the x and y axis similar to a 180 degree rotation about the origin?
yup.
What are the coordinates of the point (-10-3) after a 180 degree clockwise rotation about the origin?
To rotate the point (-10, -3) 180 degrees clockwise about the origin, you can apply the transformation that inverts both coordinates. The new coordinates will be (10, 3). Therefore, after the rotation, the point (-10, -3) becomes (10, 3).
What is the image of (5 4) when it is rotated 180 degrees about the origin?
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).
What transformation gives the same result as a rotation of 180 around the origin followed by a reflection over the y axis?
A rotation of 180 degrees around the origin followed by a reflection over the y-axis is equivalent to a single transformation: a reflection over the x-axis. This is because the 180-degree rotation negates both the x and y coordinates, and the subsequent reflection over the y-axis negates the x-coordinate again, resulting in a reflection over the x-axis.
What transformation gives the same result as a rotation of 180 around the origin followed by a reflection over the x axis?
Reflection in the y-axis.
How do you rotate 180 degrees counter clockwise about origin?
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.
What is an 180 degree rotation?
A 180-degree rotation is a transformation that turns a shape or point around a center point (often referred to as the origin) by half a full turn, resulting in the shape or point being flipped to the opposite side. For a point (x, y), the new coordinates after a 180-degree rotation will be (-x, -y). This type of rotation effectively mirrors the object across the center point. It is commonly used in various fields, including geometry, computer graphics, and robotics.
