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0/2 points Previous Answers HoltLinAlg2 6.3.014.Determine the rotation and dilation for As~/rotation1.2949radiansdilation28011ViewirSubmit AnswerPractice Another ...

Question

0/2 points Previous Answers HoltLinAlg2 6.3.014.Determine the rotation and dilation for As~/rotation1.2949radiansdilation28011ViewirSubmit AnswerPractice Another Version

0/2 points Previous Answers HoltLinAlg2 6.3.014. Determine the rotation and dilation for As ~/ rotation 1.2949 radians dilation 28011 Viewir Submit Answer Practice Another Version



Answers

Rotating a Circle Show that the equation
$$x ^ { 2 } + y ^ { 2 } = r ^ { 2 }$$
is invariant under rotation of axes.

We have given increasing thirties 30 for excess square minus 20 ful x Y plus port iWon. Why s square minus 25 is equal to zero. We have right the appropriate Robison form blood so that in a rotated system visit Chris and has no accidents y de stream. That's why we compare it first. With external prison, Biggert is equal to 34. B is equal to minus 20 for C is equal toe. For even now we will find the very low court rotator that is a minus. C Directed by B. We get 30 for minus 40 even divided by minus 24 are presently because And we get minus seven. Divided by minus 24. That is equal toe seven divided way 24. No, since Ceuta is all of his acute and court rotator is positive. That's why rotator is in first Cordant. Now we will find the value off the third side off, right? Triangle using category. Um told him we have seven square plus 24 square is equal to our square. Biggert R squared is equal to 6 25% politicus and we get our is equal to 25 Now we will find a very off course rotator that is equal to seven, divided by 25. Now we have to find the very top scientist and Wall Street are using quashed Twitter. We know that Santa is equal to the square. Root off one minus cause rotator divided by toe that is equal toe square root off one minus seven do anyway. 20 have divided by a toe. Our per simplification we get. This is equal to three, divided by five and cost Yuta. It's equal toe a square. Root off one plus course to treat are divided by a so that is equal to the square. Root off one plus seven divided by 25 divided by toe Upper simply because and we get to this is equally true for the value by fire. Now X is equal toe Xs course traitor minus writers sine theta that is equal. It'll extra s multiplied by four divided by five minus. Why there's multiplied by three Divided by five per simply because and we get X is equal toe four X desk minus three. Why there's divided by five and VIII is quarto. Next day's signed Teuta plus Vitus course Cheetah that is equal toe Xs multiplied by three, divided by five plus providers. Murder operated by poor, divided by five opera. Simply because and we get Y is equal to three Extras plus four why they're divided by 25 here. X and Y are the appropriate groups and formula, so that in a record assistant, the prison has no accidents. Where this

We know that we're dividing the white coordinates. In other words, we're doing 2/3 divided by one sex, which is 2/3 times six over one. Remember, you do the reciprocal when you're dividing fractions. Therefore, we end up with troll over three, which is equivalent to four, which is our skills, doctor. And then we know.

Ever enough you formulas here on the right side of our screen, the top to our the formulas from this section to get our rotation and our new formulas and have also put in here 1/2 angle formula from trigonometry, which we will be needing. So let's start with the co tangent of two fada. And that is a which is the coefficient of R X squared term minus C, which is equal efficient of the Y squared term, all divided by B, which is the coefficient of the X Y term. So this will get us negative seven over negative 24 or 7/24. So now I will go ahead and trust a triangle. And here is my tooth data. And the reason I'm doing this is we 7/24 is not a known value for the coat engine. So we will need to calculate out our sign and co sign right co tangent. Is Jason over opposite? So I have 7/24 and this is a Pythagorean triple 7 24 25 All right, now, from here, this is where our half angle formula comes into play. We really don't need to know the exact angle. We just need to know the value of the sign of data and the coastline of data. So here, sign North. Data is the square root of one minus. Now, from our triangle, we can see the co sign of tooth. Ada is seven over 25. So putting that into our formula over to will give us the square root of 18/25 divided by two, which is a square root of 9/25 which is 3/5. So the value of their sign of Fada is 3/5. Now the sign is the opposite over our iPod news. And here we have another refinery in Triple another 345 triangle. So from here we see the coastline of Fada is for over five. All right, we have everything we need. Let's go ahead and put together our formulas. So for X, we have ex prime time, the co sign of data for over five minus y prime times a sign of data which is 3/5. And go ahead and write. Rewrite that. Good. Now let's figure out why. Ex prime sign of data is 3/5 First. Why prime times the coastline of data, which is for over five. And we will be right this again. Ships. And there we have our two formulas.

So here is our point. Negative to zero. And we want to do a 90 degree rotation that 90. Your rotation will take this and rotated 90 degrees clockwise around the, um, coordinate system here. So instead of being out to the left, you know, like a clock and 90 degree angle would end up on the other axis up here, the Y axis. This would be up here at zero comma to so this is the coordinate.


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