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So the image (that is, point B) is the point (1/25, 232/25). Recall that A is the point (2,9).ī = C + (C - A) = (51/50 + 51/50 - 2, 457/50 + 457/50 - 9) = (1/25, 232/25). Learn the rules for rotation and reflection in the coordinate plane in this free math video tutorial by Marios Math Tutoring.0:25 Rules for rotating and ref. So the intersection of the two lines is the point C(51/50, 457/50). Usually they take pity on students, and do reflections in vertical or horizontal lines (or. Rotation says: every point moves along a circle centered at the axis of rotation, passing through the point. move directly to the reflection line, then move an identical distance past the line. 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. Reflection says: every point moves to its reflection, i.e. To transform 2d shapes, it is an easy method. These are basic rules which are followed in this concept. Transformations could be rigid (where the shape or size of preimage is not changed) and non-rigid (where the size is changed but the shape remains the same). So the equation of this line is y = (-1/7)x + 65/7. Rotation Translation Dilation Reflection Definition of Transformations. So the desired line has an equation of the form y = (-1/7)x + b. Reflect over the x-axis: When you reflect a point across the x -axis, the x- coordinate remains the same, but the y -coordinate is transformed into its opposite (its sign is changed). 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). It is easy to see, because one half is the reflection of the other half. So we first find the equation of the line through (2,9) that is perpendicular to the line y = 7x + 2. Symmetry syn- together + metron measure Reflection Symmetry The simplest symmetry is Reflection Symmetry (sometimes called Line Symmetry or Mirror Symmetry ). 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. 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). While you got it backwards, positive is counterclockwise and negative is clockwise, there are rules for the basic 90 rotations given in the video, I assume they will be in rotations review. 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. reflection: when a ray of light bounces off a reflective surface and returns into the medium from which it originated.
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