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If the signs of the Cartesian coordinates are: (+, +) => first quadrant (-, +) => second quadrant (-, -) => third quadrant (+, -) => fourth quadrant. If one of the coordinates is 0 then the point is on an axis and NOT in a quadrant. If both coordinates are 0 then the point is at the origin. If the location of the point is given in polar coordinates, then you only need the angle. Suppose the principal angle is Φ, then 0 < Φ < 90 degrees => first quadrant 90 < Φ < 180 => second quadrant 180 < Φ < 270 => third quadrant 270 < Φ < 360 => fourth quadrant. Again, if the angle is 90, 180 etc degrees, the point is on an axis. If the magnitude is 0 then the point is at the origin.
No, a triangle does not have point symmetry. Point symmetry occurs when an object or shape remains the same after being rotated 180 degrees around a central point. In the case of a triangle, it does not have point symmetry because it does not look the same after a 180-degree rotation.
If a point is at coordinates (x , y), then move it to (-x, -y).
THE LINE REMAINS PARELL ONLY IF ROTATED IN 180
It will be 180 degrees
Rotating it about the origin 180° (either way, it's half a turn) will transform a point with coordinates (x, y) to that with coordinates (-x, -y) Thus (2, 5) → (-2, -5)
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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.
The line segments will have been rotated by 180 degrees.
depending on the graph where point Q was you would not be able to tell where point Q ended after the rotaion finshed
Think of any figure, with any shape, on the graph with the origin inside the shape.Now think of any point inside the shape (except the origin).Now, in your imagination, slowly and carefully turn the shape 180 degrees around the origin ...as if it were stuck to the origin with a pin, and you gave it 1/2 turn on the pin.What happened to the point you were thinking of ?If the point started out some distance to the right of the y-axis, it wound up the same distanceto the left of the y-axis.And if it started out some distance above the x-axis, it wound up the same distance below the x-axis.So ... any point that starts out at the coordinates ( x , y ) before the 1/2 turn, winds upat the coordinates ( -x , -y ) after the 1/2 turn.
If the signs of the Cartesian coordinates are: (+, +) => first quadrant (-, +) => second quadrant (-, -) => third quadrant (+, -) => fourth quadrant. If one of the coordinates is 0 then the point is on an axis and NOT in a quadrant. If both coordinates are 0 then the point is at the origin. If the location of the point is given in polar coordinates, then you only need the angle. Suppose the principal angle is Φ, then 0 < Φ < 90 degrees => first quadrant 90 < Φ < 180 => second quadrant 180 < Φ < 270 => third quadrant 270 < Φ < 360 => fourth quadrant. Again, if the angle is 90, 180 etc degrees, the point is on an axis. If the magnitude is 0 then the point is at the origin.
If the point (3,5) is rotated 180 degrees, it becomes (-3,-5).
180 degrees.
If the point (3,5) is rotated 180 degrees, it becomes (-3,-5).
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.
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.