I like to do rotations with matrices. Let R_theta = the matrix with cos theta -sin theta sin theta cos theta Where theta is the angle of rotation So in your case, theta is 90 degres and cos 90=0, sin 90=1 so the matrix becomes 0 -1 1 0 Take any point, say (a,b) and multiply it by that matrix |0 -1| a|=(-b,a) 1 0| |b| So (1,0) becomes (0,1) and (-1,0) becomes (0,-1) ( 1,1) becomes (-1,1) Sadly the matrix stuff does not work well here, but the end result was (a,b) rotates to (-b,a)
When u rotated a figure 180 is the reflection the same
The formula is (x,y) -> (y,-x). Verbal : switch the coordinates ; then change the sign of the new x coordinate. Example : (2,1) -> (1,-2)
A rotation is a transformations when a figure is turned around a point called the point of rotation. The image has the same lengths and angle measures, and differs only in position. Rotations that are counterclockwise are rotations of positive angles. All rotations are assumed to be about the origin. R90 deg (x, y) = (-y, x) R180 deg (x, y) = (-x, -y) R270 deg (x, y) = (y, -x) R360 deg (x, y) = (x, y)
It still has the same weight. Even turned or reflected the weight/mass remains the same.
It's when a figure is rotated, reflected , translated etc but the corresponding angles and side lengths stay the same.
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
The formula is (x,y) -> (y,-x). Verbal : switch the coordinates ; then change the sign of the new x coordinate. Example : (2,1) -> (1,-2)
Center of rotation
Point of rotation
how does translation a figure vertically affect the coordinates of its vertices
well if you rotated it upside down then it would be a face with a uni brow.
A figure can be rotated through any angle of your choice.
It is called a rotation.
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.
The y-coordinates.The y-coordinates.The y-coordinates.The y-coordinates.
Translated means "slide." The y coordinates are increased