And the last thing is you can kind of consider this a flip that will be the non mathematical way of describing a reflection.
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There are 3 types of reflections that you need to know about in regards to the order pair rules. The first one is xy is mapped onto -x, y. Well to figure out what type of reflection this is let's write a little, draw a little sketch here, so I'm going to make an x axis and a y axis and I'm just going to pick some random point in the first quadrant here and we're going to call this point a and let's say point a has x coordinate 3 and y coordinate 5.
Now according to this order pair rule I'm going to take my x and takes its opposite and I'm going to keep my y exactly the same so the opposite of 3 is going to be -3 so I'm going to have to write my new image a prime over on this side of the y axis so what is our line of reflection? Well it's pretty clear that a kept the same y coordinate but it's x coordinate was taken the opposite of so we're going to categorize this as reflection over the x axis excuse me y axis.
What is reflection?
I was thinking that the x coordinates changed but since the x coordinates are changing that means that the y axis is our line of reflection. Secondly we have xy is mapped onto x and -y which means if we go back to our original point, x is going to stay the same and our y is going to be taken the opposite of so the opposite of 5 would be -5 so now our point a double prime is going to be at 3,-5 so it looks like our line of reflection is the x axis so what we're saying reflection over the x-axis. The final one that you should know by heart is xy is mapped onto yx.
What this one does, it takes every x coordinate and then makes that into a y coordinate and does the same for your y coordinates, every y coordinate becomes an x coordinate so if we have a, our a since we have a prime and a double prime our a triple prime is going to be at 5, 3 so what I'm going to do is I'm going to write 3, 5 right here.
LAWS OF REFLECTION OF LIGHT
So that way in your quiz when your teacher says what does this mapping do x, y -xy well you can say it's going to be reflected over y axis. This one when you keep x the same and take the opposite of y you know that's a reflection over the x axis and last when you switch the x's and y's that will reflect it over line y equals x. The angle of incidence is always equal to the angle of reflection.
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It means that during the reflection of light if the angle of incidence is 25 0 then the angle of reflection will also be 25 0. And if the angle of incidence is 60 then the angle of reflection will also be 60 0.
laws of reflection
The incident ray, the normal at the point of incidence of mirror and the reflected ray, all lie in the same plane. 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. If you forget the rules for reflections when graphing, simply fold your paper along the x -axis the line of reflection to see where the new figure will be located.
Or you can measure how far your points are away from the x -axis to locate the new points, such as B is 4 vertical units above the x -axis, so B' will be 4 vertical units below the x -axis. When you reflect a point across the y -axis, the y- coordinate remains the same, but the x -coordinate is transformed into its opposite its sign is changed.
Notice that B is 5 horizontal units to the right of the y -axis, and B' is 5 horizontal units to the left of the y -axis. Remember that each point of a reflected image is the same distance from the line of reflection as the corresponding point of the original figure. The line of reflection will lie directly in the middle between the original figure and its image.
While any point in the coordinate plane may be used as a point of reflection, the most commonly used point is the origin.
Reflection Over y = -2 With Rule
Assume that the origin is the point of reflection unless told otherwise. Imagine a straight line connecting A to A' where the origin is the midpoint of the segment. When you reflect a point in the origin, both the x- coordinate and the y -coordinate are negated their signs are changed. Transformations: Reflections MathBitsNotebook.