No matter how you rotate your right hand, the positive direction of the z axis is determined by the right-hand rule. The position of the middle finger is of decisive importance. To find B, extend the line AB through A to B’ so that. In this case, since A is the point of rotation, the mapped point A’ is equal to A. A point that rotates 180 degrees counterclockwise will map to the same point if it rotates 180 degrees clockwise. By virtue of the right-hand rule, your thumb becomes the positive x axis, the index finger, which is at a right angle from the thumb, becomes the positive y axis and the middle finger becomes the z axis. Because the given angle is 180 degrees, the direction is not specified.
Some of the most useful rules to memorize are the transformations of common angles. Spread the first three fingers of your right hand, as seen on the right. There are many important rules when it comes to rotation. To be able to determine the directions of the axes and the order of the x, y and z axes, the right-hand rule is applied: The associated z axis is perpendicular to both the x axis and the y axis, as can be seen in the figure on the right. learn about reflection, rotation and translation, Rules for performing a reflection across an axis, To describe a rotation, include the amount of rotation, the direction of turn and the center of rotation, Grade 6, in video lessons with examples and step-by-step solutions. Thus, in order to be able to specify a point on a part in space, in addition to the x and y coordinates, another one is needed: the z coordinate. Thus, every part, apart from its length and width, also has a height. However, the reality is three-dimensional and so is the position of objects in space. Up to now, we have only looked at coordinate systems on the drawing plane, that is, in two-dimensional space.