Plot each point, and then plot the points that are symmetric to t...

Question

Plot each point, and then plot the points that are symmetric to the given point with respect to the (a) x-axis, (b) y-axis, and (c) origin. (-4, -2)

Accepted Answer

Hello everybody. I hope we're doing right today that we're going to be looking at this question that states in one Cartesian plane show where the point P negative six comma negative one lies and also show the other points that are A, that, that are symmetric to it with respect to A, the X axis B, the Y axis and C the origin. No, the answer to is provided are four different routes. A having the points A at six comma one B six comma negative one and C negative six comma one B the point A at six comma negative one B at six comma one and C at negative six comma comma positive one, C the point A at six comma one B at negative six comma one and C at six comma negative one and D the point A at negative six comma one B at six comma negative one and C at six comma one. No. When I look at this question, the first thing I'm gonna write, it's just so we can remember is the point they gave us. So it's negative six comma negative one will be our point of reference. No, we are asking or they are asking us part A part B and part C. So let's go for part by part and start solving each one. So part A is reflection about around or about the X axis. So the X axis has a rule where basically if you have the point X comma Y that will change to the point X comma negative one. So if we have negative six comma negative one, our point will now be negative six comma positive one. So the negative six or the X stays the same and the one or, and the Y value or the negative one is multiplied by negative one. So that will be our point A or point B which is reflected about the Y axis has another rule or another way to look at it where if we have the point X comma Y and that is reflected about the Y axis, it will turn into negative X comma Y. So once again, if we have our point at negative six comma at negative one, it will turn into positive six comma negative one. So the Y in this case stays the same, but the X is multiplied by negative one. And finally, we have part C or the origin. So the origin also as a rule that we can use. So let's say you have the point X comma Y that will undergo a transformation to negative X comma negative Y or if we have our point at negative six comma negative one, it'll turn into positive six comma positive one. So they both the XX and the Y get multiplied by negative one. And it makes sense because when you're rotating about the X axis, you have to think about, if you have a point above the x axis, the X axis just acts kind of as a mirror. So if you reflect it above that, it'll have the same Y just negative. And you can use the same idea as with the Y axis. But instead now the mirror will be the Y axis. So the X will change into the other sign. So now that we have our points for A for B and for C, we can look at the graphs provided and we will see that answer choice D bits are description. They have the point A or when rotated about the X axis is negative six comma one point B when rotated about the Y axis is six comma negative one and point C when rotated about the origin six comma one. So answer choice D will be the answer to our question. So I hope that was helpful. And until next time.

Plot each point, and then plot the points that are symmetric to the given point with respect to the (a) x-axis, (b) y-axis, and (c) origin. (-4, -2)

Key Concepts

Symmetry with respect to the x-axis

Symmetry with respect to the y-axis

Symmetry with respect to the origin

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