Rules of rotation geometry xy yx verification#

The reflection of the point (x, y) over the line y = -x is the point (-y, -x).Įxample: When point Q with coordinates (6, 1) is reflecting over line y = -x and mapped onto point Q’, the coordinates of Q’ are (-1, -6). Reflection in the y = -x: Reflecting a point over the line y = -x, the x-coordinate and the y coordinate change places and the signs are changed (negated).

The reflection of the point (x, y) over the line y = x is the point (y, x).Įxample: When point Q with coordinates (1, 3) is reflecting over the line y = x and mapped onto point Q’, the coordinates of Q’ are (3, 1). Reflection in the y = x: Reflecting a point over the line y = x, the x-coordinate and the y-coordinate change places. The reflection of the point (x, y) over the line y-axis is the point (-x, y).Įxample: When point Q with coordinates (4, 5) is reflecting over the y-axis line and mapped onto point Q’, the coordinates of Q’ are (-4, 5). Reflection in the y-axis: Reflecting a point over the line y-axis, the y-coordinate remains the same, but the sign of x-coordinate is changed. The reflection of the point (x, y) over the line x-axis is the point (x, -y).Įxample: When point Q with coordinates (2, 3) is reflecting over the x-axis line and mapped onto point Q’, the coordinates of Q’ are (2, -3). Reflection in the x-axis: Reflecting a point over the line x-axis, the x-coordinate remains the same, but the sign of y-coordinate is changed. An object and its reflection have the same size and shape, but the figure faces in opposite directions. The original object is called the pre-image, and the reflection is called the image. Line reflection is folding or flipping an object over a mirror line (line of reflection). Transformation Math Examples Line Reflections What are line reflections? Here are the 5 types of transformations in math uses in geometry.

Rules of rotation geometry xy yx verification#

Transformation sets the foundation for other areas of study, such as congruence and similarity, the verification of perpendicular segments, the derivation of the equation of a circle etc. Transformations are quite important in many fields, such as the study of art, architecture, anthropology, and many more. The opening and closing of an artificial heart valve to control blood flow.Combined twist and turns of a roller-coaster.Transformations are useful in many real-world scenarios.

Transformations are movements through space and it can be seen in many instances like diverse actions walking and running. Transformations are functions that take each point of an object in a plane as inputs and transforms as outputs (image of the original object) including translation, reflection, rotation, and dilation. Transformation Math Rules Characteristics The object in the original position (before transformation) is called the pre-image and the object in the new position (after transformation) is called the image. Definition: A Transformation in Math is a process of moving an object (two-dimensional shape) from its original position to a new position.