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Current time:0:00Total duration:5:41

Determining reflections (advanced)

CCSS.Math:

Video transcript

we're asked to use the reflection tool to define a reflection that will map line segments Emme line segments Emme on to the other line segments below so we want to map Emme to this segment over here and we want to use a reflection let's see let's see what they expect from us if we want to add a reflection so if I click on this it says reflection over the line from and then we have two coordinate pairs so they want us to define the line that we're going to reflect over with two points on that line so let's see if we can do that and to do that I think I needed to write something down so let me get my let me get my scratch pad out and I copied and pasted the same diagram and the line of reflection one way to think about we want to map point E we want to map point E to this point right over here we want to map point M to this point over here and so between any point and its corresponding point on it's on the image after the reflection these should be equidistant from the line of reflection this and this should be equidistant from the line of reflection this and this should be e and this point should be equidistant from the line of reflection or another way of thinking about it that line of reflection should contain the midpoint between these two magenta points and it should contain the midpoint between these two deep navy blue points so let's just calculate the midpoints so we could do that with a little bit of mathematics the coordinates for a right over here that is let's see that is x equals negative 4 y is equal to negative 4 and the coordinates for the corresponding point to e in the image this is X is equal to 2 X is equal to 2 and Y is equal to negative 6 so what's the midpoint between negative 4 negative 4 and 2 comma negative 6 well you just have to take the average of the x's and take the average of the Y's let me do that I'll actually I'll do it over here so if I take the average of the x's it's going to be negative 4 negative 4 plus 2 plus 2 over 2 that's the average of the x's and then the average of the Y's it's going to be negative 4 plus negative 6 over 2 negative 4 plus negative six over two and then close the parentheses let's see negative four plus two is negative two divided by two is negative one so it's going to be negative one comma negative four plus negative six that same thing is negative four minus six which is going to be negative 10 divided by 2 is negative five is let me do that in a blue color so you see where it came from is going to be negative five so there you have it that's going to be the midpoint between e and the corresponding point on its image so let's see if I can if I can plot that so this is going to be this point right over here is going to be negative one comma negative five so X is negative 1 Y is negative 5 so it's this point right over here and it does indeed look like the midpoint it looks like it's equidistant between E and this point right over here and so this should sit on the line of reflection so now let's find the midpoint between em and this point right over here the coordinates of M are X is negative 5 and y is equal to 3 the coordinates here are X is equal to 7 and Y is equal to negative 1 so the midpoint that the x-coordinate of the midpoints going to be the average of the x's here so let's see it's going to be negative 5 plus 7 over 2 and the y coordinate of the midpoint is going to be the average of the y-coordinates so 3 plus negative 1 over 2 let's see negative 5a plus 7 is positive 2 over 2 is 1 3 minus 1 3 plus negative 1 that's positive 2 over 2 is 1 so the point 1 comma 1 is the midpoint between these two so 1 comma 1 just like that so the line of reflection is going to contain these two points and two points define a line in fact I could let me draw the line of reflection just because we did all of this all of this work the line of reflection is going to look something like is going to look something like I did I want to draw it a little bit straighter than that it's going to look something like it's going to look something like something like this and this makes sense that this is a line of reflection and I missed that magenta point a little bit so let me go through the magenta point okay there you go this makes sense that this is a line of reflection because you see that every you pick an arbitrary point on segment Emmy say that point and if you reflect it over this line it's this this is its shortest distance from the line you just go on to the other side of the line an equal distant and you get to this corresponding point on the image so it makes a lot of sense that these are mirror images if this is kind of the the mirror here you can imagine that this is you know this is kind of the surface of the water if you're looking at it at an angle I don't know if that helps you or not but anyway we found two points we found two points that define that line of reflection so now let's use the tool to type them in one is negative one negative five the other one is one comma one so let me see if I can remember that I have a bad memory but so one is negative one comma negative five and then the other one is one comma one and we see it worked we see it worked by when I did that it actually made the reflection happen and notice it completely went from this point and now our blue is over the image that we wanted to get to so we are we are done