![]() Now, we know that 90° clockwise rotation will make the coordinates (x, y) be (y, -x). 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. Solution: Given coordinate is A (2,3) after rotating the point towards 180 degrees about the origin then the new position of the point is A’ (-2, -3) as shown in the above graph. So, for the point K (-3, -4), a 180° rotation will result in K’ (3, 4). Put the point A (2, 3) on the graph paper and rotate it through 180° about the origin O. Solution: As we know, 180° clockwise and counterclockwise rotation for coordinates (x, y) results in the same, (-x, -y). When describing the direction of rotation, we use the terms clockwise and counter clockwise. Rotations can be described in terms of degrees (E.g., 90° turn and 180° turn) or fractions (E.g., 1/4 turn and 1/2 turn). Show the plotting of this point when it’s rotated about the origin at 180°. When describing a rotation, we must include the amount of rotation, the direction of turn and the center of rotation. When you spin the toy or figure, it keeps facing the same way, but its. The spot where it turns, or spins, is the center of rotation its like the middle point of a merry-go-round. Imagine you have a toy or a figure, and youre turning it around on the spot. It will look like this:Įxample 3: In the following graph, a point K (-3, -4) has been plotted. 'Rotation' means turning around a center: The distance from the center to any point on the shape stays the same. Rotations in Geometry are like spinning something around a central point. ![]() 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).
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