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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).
Find a 90 degree counterclockwise rotation?
follow this formula (x,y)->(-y,x)
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.
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 is image of point 4 3 if rotation is 90?
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 transformation f x y y x is what degree rotation?
90 degree anticlockwise.
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).
Find a 90 degree counterclockwise rotation?
follow this formula (x,y)->(-y,x)
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.
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 is image of point 4 3 if rotation is 90?
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).
Which transformation will be equivalent to rotating a figure 90 counterclockwise?
An equivalent transformation to rotating a figure 90 degrees counterclockwise can be achieved by reflecting the figure across the line (y = x) and then reflecting it across the x-axis. This combination of reflections results in the same final orientation as the 90-degree counterclockwise rotation.
What transformation is represented by the rule (x y) (y -x)?
It is an anticlockwise rotation through 90 degrees.
What degree clockwise rotation goes from xy to -xy?
180 degrees in the plane perpendicular to the xy plane. In general, no rotation in the (x, y) plane will take it to (-x, y) unless x = y (or -y) and, in that case it is a 270 degree clockwise rotation.
Does a transformation ever change the shape of a figure?
Yes. The transformation from y = f(x) to y=f(2x) will compress the shape along the x-axis by a factor of 2.
The equation of rotation geometric transformation?
In two dimensions, the equations of rotation about the origin are: x' = x cos t - y sin t y' = x sin t + y cos t. where t is the angle of rotation, counterclockwise.
What does a 90 degree rotation look like?
A 90-degree rotation involves turning an object or point around a fixed pivot point, such as the origin in a coordinate system, by a quarter turn. In a clockwise direction, for instance, the point (x, y) would move to (y, -x), while in a counterclockwise direction, it would move to (-y, x). This transformation changes the orientation of the object without altering its shape or size.
