![]() ![]() The angle of rotation should be specifically taken. The following basic rules are followed by any preimage when rotating: Generally, the center point for rotation is considered ((0,0)) unless another fixed point is stated. The algebraic rule for a figure that is rotated 270° clockwise about the origin is (y, -x). There are some basic rotation rules in geometry that need to be followed when rotating an image. Therefore, the algebraic rule for a figure that is rotated 270° clockwise about the origin is (y, -x) Therefore, the coordinate of a point (3, -6) after rotating 90° anticlockwise and 270° clockwise is (-6, -3). Rotating 270° clockwise, (x, y) becomes (y, -x) Rotating 90° anticlockwise, (x, y) becomes (-y, x) Given, the coordinate of a point is (3, -6) What will be the coordinate of a point having coordinates (3,-6) after rotations as 90° anti-clockwise and 270° clockwise? Rotating a figure 270 degrees clockwise is the same as rotating a figure 90 degrees counterclockwise. A rotation is an example of a transformation where a figure is rotated about a specific point (called the center of rotation), a certain number of degrees. For a rotation rO r O of 90° centered on the origin point O O of the Cartesian plane, the transformation matrix is 0 1 1 0 0 1 1 0. The line of reflection can be on the shape. The rule of a rotation rO r O of 270° centered on the origin point O O of the Cartesian plane in the positive direction (counter-clockwise), is rO: (x, y) (y, x) r O: ( x, y) ( y, x). The line that a shape is flipped over is called a line of reflection. Remember, it is the same, but it is backwards. The amount of rotation is called the angle of rotation and it is measured in degrees. In geometry, a transformation is an operation that moves, flips, or changes a shape to create a new shape. After a shape is reflected, it looks like a mirror image of itself. The fixed point is called the center of rotation. Now, we know that 90° clockwise rotation will make the coordinates (x, y) be (y, -x).What is the algebraic rule for a figure that is rotated 270° clockwise about the origin?Ī rotation is a transformation in a plane that turns every point of a preimage through a specified angle and direction about a fixed point. Solution: As you can see, triangle ABC has coordinates of A(-4, 7), B(-6, 1), and C(-2, 1). Rotate the triangle ABC about the origin by 90° in the clockwise direction. We can show it graphically in the following graph.Įxample 4: The following figure shows a triangle on a coordinate grid. So, for the point K (-3, -4), a 180° rotation will result in K’ (3, 4). Solution: As we know, 180° clockwise and counterclockwise rotation for coordinates (x, y) results in the same, (-x, -y). ![]() Furthermore, note that the vertex that is the center of the rotation does not move at all. Rotations dont distort shapes, they just whirl them around. Notice that the distance of each rotated point from the center remains the same. Show the plotting of this point when it’s rotated about the origin at 180°. In geometry, rotations make things turn in a cycle around a definite center point. While we can rotate any image any amount of degrees, 90 90, 180 180 and 270. ![]() The lines drawn from the preimage to the center of rotation and from the center of rotation to the image form the angle of rotation. It will look like this:Įxample 3: In the following graph, a point K (-3, -4) has been plotted. A rotation is a transformation where a figure is turned around a fixed point to create an image. So, for this figure, we will turn it 180° clockwise. Solution: We know that a clockwise rotation is towards the right. The images are represented in the following graph.Įxample 2: In the following image, turn the shape by 180° in the clockwise direction. Thus, for point B (4, 3), 180° clockwise rotation about the origin will give B’ (-4, -3). In the figure below, one copy of the octagon is rotated 22. Similarly, for B (4, 3), 90° clockwise rotation about the origin will give B’ (3, -4).ī) For clockwise rotation about the origin by 180°, the coordinates (x, y) become (-x, -y). In geometry, rotations make things turn in a cycle around a definite center point. Example 1: Find an image of point B (4, 3) that was rotated in the clockwise direction for:Ī) As we have learned, 90° clockwise rotation about the origin will result in the coordinates (x, y) to become (y, -x). ![]()
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