Now, we know that 90° clockwise rotation will make the coordinates (x, y) be (y, -x). Now when we rotate point A (x, y) 90 clockwise about the origin, the point becomes point A’ (-y, x). Solution: As you can see, triangle ABC has coordinates of A(-4, 7), B(-6, 1), and C(-2, 1). What are Clockwise and Counterclockwise Rotations for the Coordinates (x, y) for a Movement of 90, 180 and 270 Degrees Let us assume that the coordinates (x, y) have their center of rotation located at the origin (0, 0). 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). y xsin + ycos EQUATIONS OF ROTATION If a point (x, y) on the Cartesian plane is represented on a new coordinate plane where the axes of rotation are formed by rotating an angle from the positive x -axis, then the coordinates of the point with respect to the new axes are (x, y).
0 Comments
Leave a Reply. |