6/8/2023 0 Comments Reflection over the y axisTriangle ABC is reflected across the line y = x to form triangle DEF. Reflection over y = xĪ reflection across the line y = x switches the x and y-coordinates of all the points in a figure such that (x, y) becomes (y, x). All of the points on triangle ABC undergo the same change to form DEF. ![]() Triangle DEF is formed by reflecting ABC across the y-axis and has vertices D (4, -6), E (6, -2) and F (2, -4). Algebraically, the ordered pair (x, y) becomes (-x, y). In a reflection about the y-axis, the y-coordinates stay the same while the x-coordinates take on their opposite sign. Triangle DEF is formed by reflecting ABC across the x-axis and has vertices D (-6, -2), E (-4, -6) and F (-2, -4). Algebraically, the ordered pair (x, y) becomes (x, -y). ![]() In a reflection about the x-axis, the x-coordinates stay the same while the y-coordinates take on their opposite signs. The most common cases use the x-axis, y-axis, and the line y = x as the line of reflection. There are a number of different types of reflections in the coordinate plane. This is true for any corresponding points on the two triangles and this same concept applies to all 2D shapes. A, B, and C are the same distance from the line of reflection as their corresponding points, D, E, and F. The figure below shows the reflection of triangle ABC across the line of reflection (vertical line shown in blue) to form triangle DEF. The same is true for a 3D object across a plane of refection. In a reflection of a 2D object, each point on the preimage moves the same distance across the line of reflection to form a mirror image of itself. The term "preimage" is used to describe a geometric figure before it has been transformed "image" is used to describe it after it has been transformed. 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. In geometry, a reflection is a rigid transformation in which an object is mirrored across a line or plane. Would become the opposite and I would end up in the fourth quadrant, and that's exactly what happened.Home / geometry / transformation / reflection ReflectionĪ reflection is a type of geometric transformation in which a shape is flipped over a line. If I'm flipping over the y-axis, my y-coordinate wouldn't change, but my x-coordinate I try to do it in my head, I would still have this So the coordinates here wouldīe four comma negative two. But what would its x-coordinate be? Well, instead of it being negative four, it gets flipped over the y-axis, so now it's gonna have a And what would its coordinates be? Well, it would have the same y-coordinate, so C prime would have a So where would that put our C prime? So our C prime would be right over there. So instead of being four to the left, we wanna go four to the ![]() So its reflection is going to be four to the right of the y-axis. So we wanna reflect across the y-axis, which I am coloring it And it's the point negativeįour comma negative two, so that might look like this. It doesn't hurt to doĪ quick visual diagram. What are the coordinates of C prime? So pause this video and see if you can figure ![]() So here they tell us pointĬ prime is the image of C, which is at the coordinates negative four comma negative two, under a Maybe we could denote that with a B prime. So if we were to reflectĪcross the x-axis, essentially create its mirror image, it's going to be five So to go from B to the x-axis, it's exactly five units below the x-axis. Alright, so this is point B, and we're going to reflect it across the x-axis right over here. The image of point B under a reflection across the x-axis. But this would be the reflection of point A across the line l. On a point right over there, and it would show up. The Khan Academy exercise, you would actually just click So if we go one, two, three, four, that would be the image of point A. And so its reflection is going to be four units to the left of l. Well, one way to think about it is point A is exactly one, two, three,įour units to the right of l. So we have our line l here, and so we wanna plot the image of here, we wanna plot the image of point A under a reflection across line l. To plot the image of point A under a reflection across the line l.
0 Comments
Leave a Reply. |