So we’re going to keep the new 𝑦-coordinates the same, but multiply the 𝑥-coordinates by negative one. And remember the effect here is on the 𝑥-coordinates. The second reflection is over the 𝑦-axis. So in the image of the three points 𝐽, 𝐾, and 𝐿, which is 𝐽 prime, 𝐾 prime, and 𝐿 prime, the 𝑥-coordinates are the same, but the 𝑦-coordinates have been multiplied by negative one. The first reflection in the 𝑥-axis multiplies the 𝑦-coordinates by negative one. So we begin with the coordinates of the three points 𝐽, 𝐾, and 𝐿. Let’s actually perform this reflection on the vertices 𝐽, 𝐾, and 𝐿. So now we’ve seen what will happen to the 𝑥- and 𝑦-coordinates after each reflection. Again, this effect on the 𝑥- and 𝑦-coordinates is a general rule that you should memorize. Therefore, this time, it’s the 𝑥-coordinate that is multiplied by negative one.
Points swap from the left to the right of the 𝑦-axis and vice versa, which means the 𝑥-values change from positive to negative or negative to positive. Again, for the general point with coordinates 𝑥, 𝑦, the 𝑦-axis is a vertical line, which means the effect of this reflection is horizontal. Now, let’s think about what happens when you reflect over the 𝑦-axis. And so this is achieved by multiplying the 𝑦-coordinate by negative one. Positive values become negative and negative values become positive. Points above the mirror line now appear below the mirror line and points below now appear above, which means it’s the 𝑦-coordinate that is being affected. The 𝑥-axis is a horizontal line, which means the effect of the reflection is vertical. This is a general rule, which you should memorize.īut to see where it comes from, just picture the effect of reflecting in the 𝑥-axis. So the point 𝑥, 𝑦 gets mapped to the point with coordinates 𝑥, negative 𝑦. Well, the effect is the 𝑦-coordinate is multiplied by negative one. So let’s think about what happens to the general point with coordinates 𝑥, 𝑦 when it’s reflected over the 𝑥-axis. We need to find another method of answering this question. And we’re asked to do this without graphing, which means we’re not supposed to plot these points on a coordinate grid and then use this to help in our answer. We are asked to find the coordinates of the images of these three points. These three points are undergoing two reflections: firstly, over the 𝑥-axis and secondly, over the 𝑦-axis. So we’re given the coordinates of three points: 𝐽, 𝐾, and 𝐿. And then you can see that indeed do they indeed do look like reflections flipped over the X axis.Given that vertices 𝐽 negative eight, eight, 𝐾 three, negative nine, and 𝐿 negative three, five form a triangle, without graphing determine their coordinates after a reflection over the 𝑥-axis first and then over the 𝑦-axis. And this bottom part of the quadrilateral gets reflected above it. So you an kind of see this top part of the quadrilateral And what's interesting about this example is that, the original quadrilateral is on top of the X axis. We have constructed the reflection of ABCD across the X axis. And we'll keep our XĬoordinate of negative two. Unit below the X axis, we'll be one unit above the X axis. If we reflect across the X axis instead of being one And so let's see, D right now is at negative two comma negative one. So this goes to negative five, one, two, three, positive four. So it would have theĬoordinates negative five comma positive four. Units below the X axis, it will be four units above the X axis. The same X coordinate but instead of being four
C, right here, has the X coordinate of negative five. The same X coordinate but it's gonna be two I'm having trouble putting the let's see if I move these other characters around. So let's make this right over here A, A prime. So, its image, A prime we could say, would be four units below the X axis. So we're gonna reflect across the X axis. So let's just first reflect point let me move this a littleīit out of the way. Move this whole thing down here so that we can so that we can see what is going on a little bit clearer. So we can see the entire coordinate axis. And we need to construct a reflection of triangle A, B, C, D. Tool here on Khan Academy where we can construct a quadrilateral.
Asked to plot the image of quadrilateral ABCD so that's this blue quadrilateral here.
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