5/11/2023 0 Comments Reflection over y axis![]() So we have the coordinates of the three points after the two reflections are □ double prime is eight, negative eight □ double prime is negative three, nine and □ double prime is three, negative five. These points are referred to as □ double prime, □ double prime, and □ double prime as they’re the images of □, □, and □ after two reflections. So we’re going to keep the new □-coordinates the same, but multiply the □-coordinates by negative one. And remember the effect here is on the □-coordinates. The second reflection is over the □-axis. So in the image of the three points □, □, and □, which is □ prime, □ prime, and □ prime, the □-coordinates are the same, but the □-coordinates have been multiplied by negative one. The first reflection in the □-axis multiplies the □-coordinates by negative one. So we begin with the coordinates of the three points □, □, and □. Let’s actually perform this reflection on the vertices □, □, and □. So now we’ve seen what will happen to the □- and □-coordinates after each reflection. Again, this effect on the □- and □-coordinates is a general rule that you should memorize. Therefore, this time, it’s the □-coordinate that is multiplied by negative one. Points swap from the left to the right of the □-axis and vice versa, which means the □-values change from positive to negative or negative to positive. Again, for the general point with coordinates □, □, the □-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 □-axis. And so this is achieved by multiplying the □-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 □-coordinate that is being affected. The □-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 □-axis. So the point □, □ gets mapped to the point with coordinates □, negative □. Well, the effect is the □-coordinate is multiplied by negative one. ![]() So let’s think about what happens to the general point with coordinates □, □ when it’s reflected over the □-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 □-axis and secondly, over the □-axis. So we’re given the coordinates of three points: □, □, and □. The end result is that the point winds up in the same spot whether you rotated 180 degrees or whether you reflected about the y and then the x axis.Given that vertices □ negative eight, eight, □ three, negative nine, and □ negative three, five form a triangle, without graphing determine their coordinates after a reflection over the □-axis first and then over the □-axis. ![]() Reflecting again about the x-axis moves the poijnt from (-7,3) to (-7,-3). Reflecting about the y-axis moves the point from (7,3) to (-7,3). Rotating another 90 degrees moves the point from (-3,7) to (-7,3). In the example, you can see tht rotqting 90 degrees moves the point from (7,3) to (-3,7). Rotating 90 degrees is not the same as reflecting about the y-axis, but when you reflect that about the x-axis, the original symmetry is restored. The following example shows what happens. You can see this using an example of the point (7.3) in the following display. When you reflect again about the x-axis, (-x,y) becomes (-x,-y). When you reflect about the y-axis, (x,y) becomes (-x,y). What happens when you rotate 180 degrees is that (x,y) becomes (-x,-y) So reflecting about the y and then about the x is the same as rotating 180 degrees. You can put this solution on YOUR website!Įven though rotating 90 degrees is not the same as reflecting about the y-axis,when you reflect again about the x-axis, it becomes the same as reflecting an additional 90 degrees.
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