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. (5, -3)

Accepted Answer

Hello everybody Aberdeen. Right today, today we're gonna be looking at this math question that says in one Cartesian plane show where the point P seven comma negative 13 lies and also show the other points that are symmetric to it with respect to the A X axis B Y axis and C the origin. So this is gonna be a three part question. So the answers that they provide us are four different C Cartesian planes with answer choice A having the answer to part A as seven comma 13, part B negative seven comma negative 13 and part C negative seven comma positive 13. Answer choice B has the answer to part A as negative seven comma 13, part B seven comma 13 and part C negative seven comma negative 13. Answer choice C has the answer to part A B negative seven comma negative 13, part B negative seven comma 13 and part C seven comma 13. And finally answer choice D has the answer to part A as negative seven comma 13 part B negative seven comma negative 13 and part CS seven comma 13. No, the point that they provided point P was seven comma negative 13. So first, we have to know where this point lies. If we have a positive X, we know that it's gonna be to the right hand side of the Y axis. So in either quadrant one or quadrant four of a Cartesian plane, and we have a negative Y. So if we have a negative Y, it's gonna be below the X axis. So if it's to the right of the Y axis and below the X axis, the only quadrant that that can be in is quadrant four. So that's where our point lies. And that's where each of the answer choices have this point being. So they are all correct in that aspect. Now, we have to think about the symmetry points, right? So part A is dealing with the X axis symmetry. When there's x axis symmetry, let's say you have a point X comma Y its symmetrical point uh about the X axis will be X comma negative Y because you're flipping it about the X axis. So you're bringing it from bottom up in this case. So that means that we would go from negative comma seven, comma negative 13, two seven comma positive 13. And that would be the answer for part A which right now would be answer choice A so far, that looks to be the only one to have it correct so far. So now let's go to the next part part me which was the Y axis. Now we're talking about the Y, the symmetry about the Y axis. Let's say once again, you have a point X comma Y that will change to negative X comma Why? Why? Because if you're flipping it about the Y axis, you're changing the sign of the X, you're going from positive axis in this case to a negative X in this case. So we would go from seven comma negative 13, two, negative seven comma negative 13. And that would be the answer to part B. And so far answer choice A also has that correct. We see that answer choice D also has it but they did not have their correct answer. Part for part A. So finally, we have to check part C and for that, I will do uh I'm gonna erase a little bit at the top just to have a little bit of more workspace. So part C it's gonna be the symmetry about the origin. So how we've worked so far, let's say we have the point X comma Y. If you flip it around the origin, you would go to negative X comma negative Y because you're flipping it around both the Y axis and the X axis because it's the origin. So you're gonna change both sides of those points. So if we had seven comma negative 13, we would now have negative seven comma positive 13 for part C which also agrees with answer choice A. So answer choice A has all three points. Correct, meaning that it's gonna be the answer to this question. So I hope that was helpful and until next time.

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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. (5, -3)