Geometry rotation rules points how to#

How to Rotate a Shape Using Tracing Paper Simply switch the x and y coordinates to get (1, 3) and then multiply the 1 by -1 to get (-1, 3). Simply switch the x and y coordinates and multiply the coordinate with the negative sign by -1.įor example, to rotate the point (3, 1) 270° clockwise, it becomes (-1, 3).

$geometry rotation rules points$

To rotate a shape 270° counter-clockwise about the origin, the coordinates (x, y) become (y, -x). To rotate shape 270° clockwise about the origin, all original coordinates (x, y) becomes (-y, x). For example, the coordinate (-1, -4), will move to (1, 4) after a 180° rotation. If a coordinate is negative, it will become positive after a 180° rotation. Simply multiply each coordinate by -1 to rotate a shape 180°. For example, a coordinate at (3, 1) will move to (-3, -1) after a 180° rotation. To rotate a shape by 180° clockwise or counter-clockwise, the rule is to replace the (x, y) coordinates with (-x, -y). To use this rule, simply switch the (3, 1) to (1, 3) and then make the 3 negative to get (1, -3). Simply switch the x and y coordinates and multiply the coordinate with the negative sign by -1.įor example, use the rule (x, y) to (y, -x) to rotate the shape 90° clockwise. To rotate a shape 90° counter-clockwise about the origin, the coordinates (x, y) become (-y, x).

To rotate shape 90° clockwise about the origin, all original coordinates (x, y) becomes (y, -x). The rules for rotating shapes using coordinates are: Rules for Rotating a Shape About the Origin When rotated, a shape remains the same distance away from the centre of rotation.

The original shape is called the object and the rotated shape is called the image. You can tell that a shape has been rotated because it is not facing the same direction as it was originally. We also need to know what angle and direction the shape is rotated in.įor example, this triangle has been rotated 90° counter-clockwise about the point. A shape is often rotated about a specific point called the centre of rotation. The size and shape do not change during rotation. Now, we know that 90° clockwise rotation will make the coordinates (x, y) be (y, -x).Rotating a shape means to change its direction by turning it. 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). Show the plotting of this point when it’s rotated about the origin at 180°. It will look like this:Įxample 3: In the following graph, a point K (-3, -4) has been plotted. 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). 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). 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).