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CCSS.Math:

we're asked to plot the image of point a under a reflection across the line L so we have our line L here and so we want to plot the image of here a point P plot the image of point a under reflection across line L well one way to think about it is point a is exactly one two three four units to the right of L and so it's reflection is going to be four units to the left of L so if we go one two three four that would be the image of point a we could maybe denote that as a prime so if you're doing this on the Khan Academy exercise you would actually just click on a point right over there and it would show up but this would be the reflection of point a across the line L let's do another example so we're here we're asked plot the image of point B under a reflection across the x-axis all right so this is point B and we're going to reflect it across the x-axis right over here so to go from B to the x-axis it's exactly five units below the x-axis one two three four five so if we were to reflect across the x-axis essentially create its mirror image it's going to be five units above the x-axis one two three four five so that's where the image would be maybe we could denote that with a B Prime we are reflecting across the x-axis let's do another example so here they tell us Point C prime is the image of C which is at the coordinates negative 4 comma negative two under a reflection across the y-axis what are the coordinates of C prime so pause this video and see if you can figure it out on your own so there are several ways to approach it it doesn't hurt to do a quick visual diagram so oh that could be my x-axis this would be my y-axis and it's the point negative 4 comma negative 2 so that might look like this negative 4 negative 2 so this is the point C right over here and we want to reflect across the Y axis so we want to reflect across the Y axis which I am coloring in and red right over here so let's see the point C is 4 to the left of the y axis so it's reflection is going to be 4 to the right of the y axis so let me do it like this so instead of being 4 to the left we want to go 4 to the right so plus 4 so where would that put our C Prime so our C prime would be right over there and what would its coordinates be well it would have the same y-coordinate so C prime would have a y-coordinate of negative 2 but what would its x-coordinate be well instead of it being negative 4 it gets flipped over the y-axis so now it's going to have an x coordinate of positive 4 so the coordinates here would be 4 comma negative 2 4 comma negative 2 you might have been able to do this in your head although for me even if I try to do it in my head I would still have this visualization going on in my head ok negative 4 comma negative 2 I'm sitting there in the 3rd quadrant if I'm flipping over the y-axis my y-coordinate wouldn't change but my x coordinate would become the opposite and I would end up in the 4th quadrant and that's exactly what happened why quiet y coordinate did not change but then my x coordinate since I'm flipping over the y-axis it became the negative of this that opposite of negative 4 which is positive 4