create a design using reflection and glide reflection

Thus there are seven possible frieze groups. By a process of elimination, these can only occur in seven possible combinations.

Because two reflection axes which meet at an angle. The only possibilities are 180 rotations, reflections with vertical axes, a reflection with horizontal axis, and a glide reflection with horizontal axis. The first crucial step is known as the crystallographic restriction : A rotation symmetry of a wallpaper pattern must be a rotation of order 2, 3, 4, or 6. The third frieze group, F 3, contains translation and vertical reflection. As with frieze groups, the classification of wallpaper symmetry groups is done by a process of elimination. According to Conway, F 2 is called a STEP. The second frieze group, F 2, contains translation and glide reflection symmetries. According to Conway, F 1 is also called a HOP. It involves both processes, but in a specific order. So the intersection of the two lines is the point C(51/50, 457/50). Mathematician John Conway created names that relate to footsteps for each of the frieze groups. Glide reflection symmetry is best thought of as a hybrid between reflection and translational symmetry. Now we need to find the intersection of the lines y = 7x + 2 and y = (-1/7)x + 65/7 by solving this system of equations. So the equation of this line is y = (-1/7)x + 65/7. Subtract 12 units from each of ABC’s x-coordinate. Now, graph ABC on the xy-coordinate plane and apply the appropriate transformations: 1. Substituting the point (2,9) givesĩ = (-1/7)(2) + b which gives b = 65/7. When working with glide reflection, expect to translate and reflect the given pre-image. So the desired line has an equation of the form y = (-1/7)x + b.

Since the line y = 7x + 2 has slope 7, the desired line (that is, line AB) has slope -1/7 as well as passing through (2,9). So we first find the equation of the line through (2,9) that is perpendicular to the line y = 7x + 2. Then, using the fact that C is the midpoint of segment AB, we can finally determine point B.Įxample: suppose we want to reflect the point A(2,9) about the line k with equation y = 7x + 2. Then we can algebraically find point C, which is the intersection of these two lines. So we can first find the equation of the line through point A that is perpendicular to line k. What combination of transformations did she use to create the. Note that line AB must be perpendicular to line k, and C must be the midpoint of segment AB (from the definition of a reflection). Graph each figure with the given vertices and its image after the indicated glide reflection. Let A be the point to be reflected, let k be the line about which the point is reflected, let B represent the desired point (image), and let C represent the intersection of line k and line AB.

Create a design using reflection and glide reflection