The line segments will have been rotated by 180 degrees.
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.
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.
It is (-1, 6).
You dont, its just 90 degrees 3 times..
(-1, -4) rotated 90 degrees anticlockwise
Negate each of the x and y components of all three vertices of the triangle. For example, a triangle with vertices (1,2), (8,3), and (5,6) would become (-1,-2), (-8,-3) and (-5,-6) when rotated 180 degrees about the origin.
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The line segments will have been rotated by 180 degrees.
add the
{1 0} {0 -1}
y = 20x is symmetric about the origin. (If you rotate it around the origin, it will look the same before it is rotated 360 degrees).
If you know how to rotate a triangle around the origin, treat the point as the origin.If you have Cartesian coordinates (that is x, y pairs) for the points of the triangle,subtract the coordinates of the centre of rotation from the coordinates of the triangle, do the rotation and then add them back on.Doing it geometrically:Draw line from centre of rotation to a point (for example a vertex)Measure the required angle from this line and draw in the rotated lineMeasure the distance from the centre of rotation to the original point and measure along the rotated line the required distance to get the rotated point.repeat for as many points as needed (eg the 3 vertices of the triangle) and join together the rotated points in the same was as the original points.[The construction lines drawn to the centre of rotation can be erased once the rotated point is found.]
Visualize a capital "N." Rotated 90 degrees counter-clockwise (a quarter turn to the left) it would look like a capital "Z."
That would depend on its original coordinates and in which direction clockwise or anti clockwise of which information has not been given.
No, only their positions will change.
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.