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When a point ((x, y)) is rotated around the origin by an angle (\theta), the new coordinates ((x', y')) can be determined using the rotation formulas: (x' = x \cos(\theta) - y \sin(\theta)) and (y' = x \sin(\theta) + y \cos(\theta)). This transformation effectively changes the point's position in a circular motion around the origin based on the specified angle. The direction of rotation (clockwise or counterclockwise) also affects the signs of the trigonometric functions used.
What else can I help you with?
In math how do rotations affect coordinates?
A rotation turns a shape through an angle at a fixed point thus changing its coordinates
What is a rotation of 90 Degrees counterclockwise?
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.
What are the coordinates of the preimage of vertex M?
To determine the coordinates of the preimage of vertex M, I would need additional information about the transformation that was applied to vertex M, such as the type of transformation (e.g., translation, rotation, reflection, scaling) and the coordinates of M itself. If you provide the coordinates of M and the details of the transformation, I can help you find the preimage coordinates.
What is meant by slope in coordinate geometry?
Rise over run, generally change in y-coordinates divided by change in x-coordinates.
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.
How can the rotation matrix be expressed in terms of spherical coordinates?
The rotation matrix can be expressed in terms of spherical coordinates by using the azimuthal angle (), the polar angle (), and the radial distance (r) to determine the orientation of the rotation.
What do you if both the coordinates are negative when doing a rotation of 90 degrees?
The answer will depend on whether the rotation is clockwise or anti-clockwise.
What information is not needed when performing a rotation?
When performing a rotation, you do not need to know the exact coordinates of the center of rotation. All you need is the angle of rotation and the shape or object being rotated.
In math how do rotations affect coordinates?
A rotation turns a shape through an angle at a fixed point thus changing its coordinates
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 are two important things gears do?
Change speed of rotation. change direction of rotation.
What is the Rotation rule for 180 counter clockwise?
The rotation rule for a 180-degree counterclockwise rotation involves turning a point around the origin (0, 0) by half a circle. For any point (x, y), the new coordinates after this rotation become (-x, -y). This means that both the x and y coordinates are negated. For example, the point (3, 4) would rotate to (-3, -4).
How do you calculate the coordinates of center of a rotation?
In the algebraic equation for a circle. (x - g)^2 + (y - h)^2 = r^2 'g' & 'h' are the centre of rotation.
Describe how to find the coordinates of the image of a point after a 270 degree rotation?
Point A has coordinates (x,y). Point B (Point A rotated 270°) has coordinates (y,-x). Point C (horizontal image of Point B) has coordinates (-y,-x).
What is meant by slope in coordinate geometry?
Rise over run, generally change in y-coordinates divided by change in x-coordinates.
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 are the coordinates of the point (1 and ndash6) after a counter clockwise rotation of 90 and deg about the origin?
The coords are (6, 1).
