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Transformation of affine space
- In geometry, a point reflection (also called a point inversion or central inversion) is a transformation of affine space in which every point is reflected across a specific fixed point.
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In geometry, a point reflection (also called a point inversion or central inversion) is a transformation of affine space in which every point is reflected across a specific fixed point. When dealing with crystal structures and in the physical sciences the terms inversion symmetry, inversion center or centrosymmetric are more commonly used.
A point reflection is just a type of reflection. In standard reflections, we reflect over a line, like the y-axis or the x-axis. For a point reflection, we actually reflect over a specific point, usually that point is the origin . Formula r(origin) (a, b) → (−a, −b) Formula r ( o r i g i n) ( a, b) → ( − a, − b) Example 1.
A reflection is a transformation that acts like a mirror: It swaps all pairs of points that are on exactly opposite sides of the line of reflection. The line of reflection can be defined by an equation or by two points it passes through. Part 1: Reflecting points. Let's study an example of reflecting over a horizontal line.
- I do not understand any of this at all. Is there an easier way to learn/understand it?Simple reflections are a matter of looking at a line and a point, line, or polygon on one side of it. You want to figure out the distance between t...
- I understand how to algebraically perform reflections if the line of reflection is y = 0, x = 0, y =...Great question! 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)...
- I could really use Sal making a video about this, what’s written on this doc is really confusing. So...The reflection line is the line that you are reflecting over. Y=mx+b is just the basic slope-intercept equation. If you don't understand slope -int...
- Is there a formula for the reflections?count the spaces between the line you are reflecting over
- I cried over this lesson for over an hour, took a 2 day break,and then cried at the thought of it. I...wow that is bonkers
- why cant there be a video on this i dont understand it but a video would helpThere is a part that says "I want to see Sal doing a similar question" which helped me since I was having trouble.
- Is there a more mathematical way of calculating the reflection as opposed to manually counting on a ...Yep, just plug the coordinates for each point into the point-slope equation that is given to get the reflected points. Eg. In the last example in t...
- This is a probably a stupid question, but i totally do not get why -- for example -- in this problem...No questions are stupid! y=-1-x and y=x are both lines. When you reflect a point, it is an equal distance away from the line as your original point...
- isn't there an algebraic formula for this ?When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordin...
We can plot points after reflecting them across a line, like the x-axis or y-axis. Reflections create mirror images of points, keeping the same distance from the line. When we reflect across the y-axis, the image point is the same height, but has the opposite position from left to right. Questions.
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- What does prime mean when for example they say C prime?In the context of geometric transformations, the prime symbol (') denotes the image of a point as a result of a transformation. For example, point...
- not as bad as rotating...rotation confuses me90° clockwise rotation: (x,y) becomes (y,-x) 90° counterclockwise rotation: (x,y) becomes (-y,x) 180° clockwise and counterclockwise rotation: (x,...
- how do you identify the reflection of -2,6 ?Depends what axis you are reflecting over, if you are reflecting over x axis, change the y positive or negative sign to the opposite sign, if it re...
- here is another reflecting video: https://www.khanacademy.org/math/basic-geo/basic-geo-transformatio...Thanks! there's actually a way to do it algebraically too, if you don't know it already you'll need it: Across the x-axis -(x,y)- (x,-y) Across the...
- can i get a little bit of explanation?Some basic rules: - Reflection over x-axis: (x, y) ---> (x, -y) - Reflection over y-axis (x, y) ---> (-x, y) - Reflection over line where y = x (x,...
- are you exposed to be in high school ? if so I'm in elementary schoolYou don't have to be in a specific grade to learn the concepts. This is done on purpose so students can learn at their own pace. With that said, do...
- Is reflecting the same thing as rotating 180 degrees about point "x" for example?That depends on the shape. In the case of a square, for example, you could rotate it 90 degrees about the center and get the same thing. However, i...
Just like looking at a mirror image of yourself, but flipped....a reflection point is the mirror point on the opposite side of the axis. Watch this tutorial and reflect :). Created by Sal Khan. Questions. Tips & Thanks. Want to join the conversation? Log in. Sort by: Top Voted. Avanay_07. 4 years ago.
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- Sal Khan
In geometry, a reflection is a rigid transformation in which an object is mirrored across a line or plane. When an object is reflected across a line (or plane) of reflection, the size and shape of the object does not change, only its configuration; the objects are therefore congruent before and after the transformation.
5 days ago · Reflection. Consider a point source of light that sends out a spherical wave toward an imaginary flat plane, as in the left diagram below. When the wave reaches this plane, then according to Huygens's principle, we can look at every point on the plane and treat it as a point source for an individual wavelet (center diagram below).
