![]() ![]() The reflection looks something like this. The real appreciation here is think about, well, what happens with I really just want you to see what the reflection looks like. Know for the sake of this video, exactly how Iĭid that fairly quickly. And so our new when we reflect over the line L. And since C is right on the line now its image, C prime, won't change. But you don't have to know that for the sake of this video. So what it essentiallyĭoes to the coordinates is it swaps the X and Y coordinates. And we can even think about this without even doing the What is preserved, or not preserved as we do a reflection across the line L. In this situation let us do a reflection. Let's do another example with a non-circular shape. To here we went to the coordinate we went to the coordinate So for example, theĬoordinate of the center here is for sure, going to change. But, they'll preserve things like angles. We don't have clearĪngles in this picture. We're transforming a shape they'll preserve things And this is in general true of rigid transformations is that they will preserve the distance between corresponding points if And you could also thatįeels intuitively right. They're gonna have all of these in common. Radius is preserved and then the area is also going to be preserved. In fact, that follows from the fact that the length of the radius is preserved. Well, if the radius is preserved the perimeter of a circle which we call a circumference well, that's just aįunction of the radius. The radius here is also is also two, right over there. Things that are preserved well, you have things like the radius of the circle. Under a rigid transformation like this rotation right over here. That are preserved or maybe it's not so clear, we're gonna hope we make them clear right now. So you got to forgive that it's not that well ![]() So our new circle, the image after the rotation might And let's say our centerĮnds up right over here. So let's say we end up right over so we're gonna rotate that way. Of argument we rotate it clockwise a certain angle. We take this circle A, it's centered at Point A. Rigid transformations which means that the lengthīetween corresponding points do not change. Think about rotations and reflections in this video. Of a shape are preserved or not preserved, as they undergo a transformation. So the image (that is, point B) is the point (1/25, 232/25).Going to do in this video is think about what properties So the intersection of the two lines is the point C(51/50, 457/50). 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. 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. ![]() 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). 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. ![]()
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