![]() This article will focus on the transformation that occurs when a triangle is rotated 90° about the origin. Various types of transformations are used in mathematics, including rotations, translations, reflections, and dilations. ![]() Transformations refer to geometric shapes that move around a plane. This means that the x-coordinate becomes the new y-coordinate, and the y-coordinate becomes the opposite of the new x-coordinate. When a triangle is rotated 90 degrees about the origin, the rule that describes the transformation is (x, y) → (-y, x). Finally, rotations can also be described as the center of rotation, a point or a line. Another way is to describe rotations in terms of the direction of rotation (e.g., clockwise or counterclockwise). One way is to describe rotations in terms of the degree measure of the angle of rotation (e.g., a 90-degree rotation, a 180-degree rotation, etc.). There are different ways to describe rotations in geometry, one of the four basic transformations (rotations, reflections, translations, and dilations). Different ways rotations can be described It plays a vital role in various mathematics, engineering, and physics fields. Understanding rotational symmetry properties also helps identify symmetric objects and fractions of rotations such as quarter turns, half turns, and full turns. By knowing this rule, one can easily perform a rotation of a triangle or any other object that exhibits rotational symmetry. This transformation involves swapping the x and y-coordinates and negating the new y-coordinate. One rule that describes the transformation of rotating a triangle 90° about the origin is (x,y) → (-y,x). It is essential to understand this property in geometry to accurately perform transformations such as rotating a triangle 90° about the origin. The property of rotational symmetry refers to the ability of an object to be rotated by a certain angle and appear unchanged. Understanding rotations and the rules that govern them is essential in geometry, where they solve various problems involving angles, shapes, and spatial relationships. To visualize this transformation, imagine a point on the triangle at coordinates (x, y) moving around the origin to coordinates (-y, x) along a circular path, with an angle of 90° between the initial and final positions. As a result, the triangle is rotated counterclockwise around the origin. This means that the x-coordinate of a point becomes its new y-coordinate, and the y-coordinate becomes its new negative x-coordinate. When a triangle is rotated 90° about the origin, the rule that describes the transformation is (x, y) → (-y, x). ![]() In geometry, rotations are measured in degrees, and the direction of the rotation depends on whether it is clockwise or counterclockwise. Rotations are transformations that move points in a plane around a fixed center point by a certain angle. Defining rotations and how they are measured ![]() In this section, we will understand the specifics of this rule and how it applies to the rotation of a triangle. For example, when a triangle is rotated 90° about the origin, it follows a specific transformation rule. Rotations in geometry involve rotating a figure or shape around a certain point. Understanding the rules of transformation is crucial in geometry to solve problems involving translations, rotations, and reflections of geometric shapes accurately. Therefore, this transformation can be applied to any triangle, regardless of size or orientation. It is important to note that a 90-degree rotation about the origin is a type of rotational symmetry, meaning the original and rotated figures are congruent. A triangle is rotated 90° about the origin. This rule involves switching the x and y-coordinates of each point and negating the new x-coordinate.įor example, if the original coordinates of a point on the triangle were (3, 4), the rotated coordinates would be (-4, 3). When a triangle is rotated 90° about the origin, the transformation rule that describes the change is (x, y) -> (-y, x).
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