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1_ An equilateral triangle with one vertex at (0, 3) has rotational symmetry about the origin. What is the length of each side of the triangle?...

Question

1_ An equilateral triangle with one vertex at (0, 3) has rotational symmetry about the origin. What is the length of each side of the triangle?

1_ An equilateral triangle with one vertex at (0, 3) has rotational symmetry about the origin. What is the length of each side of the triangle?



Answers

Construct an equilateral triangle whose sides are the given length.

3 inches

Hello students. So uh we have given the area of equilateral triangle that is 63 centimeter square. And to determine the length of the site of triangle. Using the given expression that is S. Equals two. Underwrote four Through three a upon three. So now we're going to simplify so it's A. Equals two. Underwrote for room three upon to the No. I will put the data. All right. S. A. Equals as he had done a note area and the road ford four rule three six. The road three on to the So after solving this we will get we will get in the root 72 on three which we can And it comes out to be under 24. No, we'll have to ah Simplifying this under 24 weekend night. It has underwrote four into six. So it will equal to Thunder road Food Into a little six which comes out to be too and six through the length of the side of triangles to route six centimeter. And that is your answer. Thank you.

Prime 58 covers the distance formula. It asked us to find the third verte asi of the triangle formed with one side connecting the 10.0 comma zero and zero comma four. And the triangle being an equilateral triangle. So first to sell this, we can determine that the midpoint of this line that connects zero comma zero and zero coming for we'll be right here halfway through which is the point zero comment to. So that's the midpoint of the line. So if it's an equilateral triangle, they give us that the side, the length of the side is for and an equilateral triangle all sides are equal. So we know that this side of the triangle and this side of the triangle have to equal four. We also know that the midpoint for the point of the of the verte asi the y coordinate of the vertex. See that we're trying to find has to equal to because it has to lie on this line which is the line Y equals two. So to solve this using the distance formula we can plug in our values and then solve for X two which will be the X component of our verte asi. So we'll go ahead and plug in our values. We know that our distance now that our distance we for let's just look at this line right here. So we know our distances for. We'll plug that into the distance formula or two points are zero comma zero and next to comma tooth because we know the Y coordinate of the vertex C. Has to equal to. So we plug in our values we have X two minus X 10 squared loss. Why to which is to minus lie 10 squared. Now we can solve for X two. So we'll continue. Yeah the square root of X two squared plus two squared. I'm to solve for X two will square both sides to get rid of the square root. So square this side and we'll swear this side. So we get 16 equals next to squared plus two squared. Or for remember when you square square root it cancels out. You can then subtract four on both sides. Yeah. X two squared equals 16 minus four or 12. And we'll take the square root to solve for X two. So perhaps too is going to equal plus or minus square root of 12 or approximately 3.46 So this will be our X coordinate and we already know are Y coordinate will be too. So we'll count 3.46 units. So we know this is too that will count 3.46123 About right here and then there's another verte asi on in quadrant two which contains the point. It would be negative 3.46 so 12 three. Yeah, right here. This is also an equilateral triangle, so we can form two equilateral triangles. And our verses will be this point, which is 3.46 Colin too, and this point as well, which will be negative 3.46 constitute.

We need to determine of the following three points are. The vertex is of an equilateral triangle. So we need to find the distance between three sets of points. So we have between negative one and negative one and two and three And then we have two and 3 And -4 and three. And then we have to do from negative 1 -1 And -4 and three. So our distance formula is the square root of the difference of the exes squared plus the difference of the wise squared. So if we label our points X one, Y one X two, Y two, we replace our values. So we have parentheses, parentheses minus sine squared plus parentheses, parentheses minus sine squared. We replace we had two minus a negative one and three minus a negative one. So our distance is equal to the square root of three squared plus four squared. So we get our distance is equal to 9-16. Where distance is equal to the square root of 25. So our distance from the first two points is five. So now we try our second two points. So we label X one Y one X two Y two. We plug into the formula. So parentheses, parentheses minus sine squared plus parentheses, parentheses minus sine squared. We get negative four and two. We get three and three. We get the distance is equal to negative six square plus zero squared r distances 36 plus zero. Our distance is equal to the square to 36. So our distance is six so there's no point in finding the distance for the next 22 set of points because if it was equal lateral, all three numbers would be the same. So this triangle is not equilateral. Yeah.

According to given question, we have an equal. It'll trigger. So let us suppose that given point a is zero comma food and another point is B, which is, you know, Commerce Joe. Now we have to check the third point that you see. So this is X comma way now, since this is equally downtrend in distance between point a common be you will can create this force so that zero miners little square less four miners little over a square. This is coming as Route four whole square. So 60 which we can say that for this does wouldn't point. You see, this is equality X minus zero. Why minus four old square. So we can say that this is coming years x squared less y minus Fuller Square on December 1 Point B. C. You can say that this is a little zero minus x squared zero minus y. This is rude under X squared this? No, since it is equilateral triangle So we can say that the square become a C Most people toe d square a comma be This is getting fuller The square Nico Massie So this is X squared plus y squared and this is must be wonderful. And we can say that the square in commerce city must be equal to the square be called mercy. So that means X squared plus y minus four. All square must be equal to X squared plus y squared. So here we can cancel X square an extra opening distant date y squared plus 16 minus it way. This is recorded words quote you can cancel away script So anyway is going at 60. That means why is coming US 16 divided by eight Metical Put to now putting the man you off Why in this? And you can see that does X squared plus white dress alike right to square is grateful for For that means every tonight this is for quiet. So here this foursquare X squared is equal to 16 minus four against X squared is going well, which is giving access acquittal bless and minus routes to it. So here we have find the one that means we have points A sequel in it can be extra Momesso Route 12 common to our minus root. Welcome, Myrtle. So does in two Bangles are possible, but this strangles, uh, was he good


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