Table of Contents
What is an algebraic rotation?
A rotation is the movement of a geometric figure about a certain point. The amount of rotation is described in terms of degrees. If the degrees are positive, the rotation is performed counterclockwise; if they are negative, the rotation is clockwise.
What is the algebraic representation of a 180 degree rotation?
The rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .
What does algebraic representation mean in math?
In mathematics, an algebraic representation of a group G on a k-algebra A is a linear representation such that, for each g in G, is an algebra automorphism. Equipped with such a representation, the algebra A is then called a G-algebra.
How do you write algebraic representation for dilation?
When a dilation in the coordinate plane has the origin as the center of dilation, you can find points on the dilated image by multiplying the x- and y-coordinates of the original figure by the scale factor. For scale factor k, the algebraic representation of the dilation is (x, y) → (kx, ky).
What is the algebraic representation of a reflection?
To reflect a figure across a line of reflection, reflect each of its vertices. Then connect the vertices to form the image. Each point and its image must be at the same distance from the line of reflection.
What is the algebraic representation of a reflection over the y-axis?
A reflection of a point over the y -axis is shown. The rule for a reflection over the y -axis is (x,y)→(−x,y) .
What is a 270 degree clockwise rotation?
Rotating a figure 270 degrees clockwise is the same as rotating a figure 90 degrees counterclockwise.
What is an example of algebraic representation?
For example, 3x + 5 = 20 is an algebraic equation where 20 represents the right-hand side (RHS), and 3x +5 represents the left-hand side (LHS) of the equation.
What are algebraic equations?
algebraic equation, statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root. Examples are x3 + 1 and (y4x2 + 2xy – y)/(x – 1) = 12.
What is the angle of rotation of a graph?
As per the definition of rotation, the angles APA’, BPB’, and CPC’, or the angle from a vertex to the point of rotation (where your finger is) to the transformed vertex, should be equal to 90 degrees. If you want, you can connect each vertex and rotated vertex to the origin to see if the angle is indeed 90 degrees.
How to draw the direction of rotation by a positive angle?
Draw the image of this rotation using the interactive graph. The direction of rotation by a positive angle is counter-clockwise. So positive is counter-clockwise, which is a standard convention, and this is negative, so a negative degree would be clockwise. And we want to use this tool here.
What is the angle of rotation of the rotated triangle?
The rotated triangle will be called triangle A’B’C’. As per the definition of rotation, the angles APA’, BPB’, and CPC’, or the angle from a vertex to the point of rotation (where your finger is) to the transformed vertex, should be equal to 90 degrees.
What determines the angle of rotation of a plane?
Every rotation is defined by two important parameters: the center of the rotation—we already went over that—and the angle of the rotation. The angle determines by how much we rotate the plane about the center.