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 distance
to 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 up
at the coordinates ( -x , -y ) after the 1/2 turn.
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.
If it's an *equilateral* triangle, a triangle. Check out quadrilaterals (squares, rectangles), then *equilateral* pentagons, hexagons, etc. Generally, an equilateral polygon needs only rotate (360/number of sides) degrees to coincide.
The image of a vertex at (x, y) would be (-y, x).
Center of rotation
Point of rotation
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.
When u rotated a figure 180 is the reflection the same
multiply the coordinates by -1.
Visualize a capital "N." Rotated 90 degrees counter-clockwise (a quarter turn to the left) it would look like a capital "Z."
If a point is at coordinates (x , y), then move it to (-x, -y).
A circle
If it's an *equilateral* triangle, a triangle. Check out quadrilaterals (squares, rectangles), then *equilateral* pentagons, hexagons, etc. Generally, an equilateral polygon needs only rotate (360/number of sides) degrees to coincide.
The image of a vertex at (x, y) would be (-y, x).
Center of rotation
Point of rotation
how does translation a figure vertically affect the coordinates of its vertices
Rotation Symmetry La Simetria de Rotation Symetrie de Rotation