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For every point A = (x,y) in your figure, a 180 degree counterclockwise rotation about the origin will result in a point A' = (x', y') where:
x' = x * cos(180) - y * sin(180)
y' = x * sin(180) + y * cos(180)
Happy-fun time fact: This is equivalent to using a rotation matrix from Linear Algebra!
Because a rotation is an isometry, you only have to rotate each vertex of a polygon, and then connect the respective rotated vertices to get the rotated polygon.
You can rotate a closed curve as well, but you must figure out a way to rotate the infinite number of points in the curve. We are able to do this with straight lines above due to the property of isometries, which preserves distances between points.
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How many degrees has triangle ABC been rotated counterclockwise about the origin?
180 degrees.
How do you rotate a figure 270 degrees clockwise around the origin?
Move it 3 times* * * * *or once in the anti-clockwise direction.
How do you rotate a figure 270 degrees clockwise about origin?
You dont, its just 90 degrees 3 times..
How do you rotate a figure 180 degrees clockwise about origin?
To rotate a figure 180 degrees clockwise about the origin you need to take all of the coordinates of the figure and change the sign of the x-coordinates to the opposite sign(positive to negative or negative to positive). You then do the same with the y-coordinates and plot the resulting coordinates to get your rotated figure.
What is the image of (1 -6) for a 90 and deg counterclockwise rotation about the origin?
It is (-1, 6).
How many degrees has triangle ABC been rotated counterclockwise about the origin?
180 degrees.
How do you rotate a polygon 90 degrees counterclockwise about the origin?
{1 0} {0 -1}
How do you rotate a figure 270 degrees clockwise around the origin?
Move it 3 times* * * * *or once in the anti-clockwise direction.
How do you rotate a figure 90 degrees counterclockwise about origin?
Ex: -1,-2 Switch the numbers, so with the example it would be -2,-1. Next multiply your x coordinate by -1,so the example would be 2,-1
What is the image of 1 -6 for a 90 counterclockwise rotation about the origin?
(-1, -4) rotated 90 degrees anticlockwise
How do you rotate a figure 270 degrees clockwise about origin?
You dont, its just 90 degrees 3 times..
How do you you rotate a figure 90 degrees clockwise about the origin?
To rotate a figure 90 degrees clockwise about the origin, simply swap the x and y coordinates of each point and then negate the new y-coordinate. This is equivalent to reflecting the figure over the line y = x and then over the y-axis.
How do you rotate a figure 180 degrees clockwise about origin?
To rotate a figure 180 degrees clockwise about the origin you need to take all of the coordinates of the figure and change the sign of the x-coordinates to the opposite sign(positive to negative or negative to positive). You then do the same with the y-coordinates and plot the resulting coordinates to get your rotated figure.
Rule for 180 degree clockwise rotation?
To rotate a figure 180 degrees clockwise, you can achieve this by first reflecting the figure over the y-axis and then reflecting it over the x-axis. This double reflection effectively rotates the figure 180 degrees clockwise around the origin.
Will the sides of the triangle change if rotate a figure 90 degrees clockwise about origin?
No, only their positions will change.
How do you rotate a figure 90 degrees counterclockwise about the origin?
Given a set of points, (x1, y1), (x2, y2), etc. Take the absolute value of each point's x and y values, and replace those. Take the inverse point of each point, e.x. (x1, y1) -> (y1, x1) Apply the signs that correspond to the quadrant counterclockwise of the quadrant the point was in. e.x. (3, 5) is in the First Quadrant. The Second Quadrant is counterclockwise of the First, so we will have the x-value of the point negative: (-3, 5). Do that for all points.
How do you reflect a figure around the origin?
The best way is this:Draw a line from the point closest to the origin to the actual origin. Rotate the line however many degrees you are told, whichever way you are told. After you have the point closest to the origin rotated, you can either rotate the other points the same way or just draw them in based on where the other point lies.Another way, sort of the cheater way, is to just take a piece of tracing paper and trace the figure onto it. Hold it down by pressing your pencil on the tracing paper where the origin is, and rotating it however many degrees, whichever way you are told.This is for ROTATE. To reflect just use the opposite signs on the coordinates.
