let-s-be-the-triangle-with-vertices-42124642-226-find-the-image-of-s-under-the-perspective-projectio

Name: let s be the triangle with vertices 42124642 226 find the image of s under the perspective projectio
Uploaded: 2019-08-12
Duration: 7 min 9 s
Channel: Numerade
Description: Let $S$ be the triangle with vertices $(4.2,1.2,4),(6,4,2),$ $(2,2,6) .$ Find the image of $S$ under the perspective projection with center of projection at $(0,0,10) .$

Question

Let $S$ be the triangle with vertices $(4.2,1.2,4),(6,4,2),$ $(2,2,6) .$ Find the image of $S$ under the perspective projection with center of projection at $(0,0,10) .$

Gideon Idumah · Accepted Answer

now looking nuts. The rights off on prospects of projection prospects. Eve projection, which is just just before example. It&#x27;s in this section just before example it&#x27;s You can go back and look at seeds. We see that the metrics peen that&#x27;s performs a prospect. Seve Projection with Sensor zero comma zero comma D is given by P equal to 1000 0100 000 minus one over D andi 001 You can go back and confirm That&#x27;s not in our example. Allah Sensa is given a zero comma zero comma 10. So when compared? This and these. This implies that r D he calls to say so. That implies that our p that sees the metrics that performs in perspective projection will be given by 10000100 000 minus one over 10 which is minor. Zero points. 10001 No, um, the marginal squadron eight. It&#x27;s what he needs Off the triangle off the triangle recorder were given the point. The boxes has four point. Sorry. 93 minus five. But if want to writing homogeneous coordinates all rights, it as so maybe written as All right, sit as 93 minus five. There we are, the one at the end rights on. Then the other one becomes 12. It&#x27;s Sue. One on the last one is one point AIDS to point several one, and they are being one. So this isn&#x27;t about Gina&#x27;s coordinates, so this implies that&#x27;s did its army trees. Your deeds are many trees for is, is given by. So you just turned this into images. You have nine three minus 51 Suave. It&#x27;s Sue 11 point. It&#x27;s super in several 11 on Also did. That&#x27;s our metrics. Guts on many trees for the chance from tango for the Transformed Triangle would then be given us. You just multiply these Petey Mitch is that before? Which is 1000 0100 000 My nose. Oh, want Juan 0001 more supplied by the determined Jizz for S, which is nine three minus 51 Suave. It&#x27;s 211 points. It&#x27;s super 2110.711 way multiplied things off. 9301.5 suave. It&#x27;s 00 point means one points. AIDS soup want 70 on, then zero points? Nine? No. Lastly, the last thing we do is that&#x27;s we convert its from the homogeneous coordinates. So the columns Oh, this matrix, come on, be converted from well with Gino&#x27;s coordinates by dividing by the final coordinates by the final Cordant record. That&#x27;s how we change from more Gino&#x27;s coordinates. So that implies that the first column, which is 9301.5, then becomes would divide everything by one points. Fine. That&#x27;s a nine over 1.5 three over 1.5 and then zero over 1.5, which is a goal to 6 to 0. Similarly swore it&#x27;s 00 Prinz Deeds becomes soften. Lazar points speeds. It&#x27;s over zero point. AIDS zero over zero point AIDS. This is 15 cents on zero and lastly, one points. Foods soup 1700.9 becomes one points. It&#x27;s over zero points. Nine super in seven over 0.9 under zero over 0.9. This is so comma zero. So this implies dots. This implies that the co ordinates off the vortices off the transforms, trying go off the transform Trying go! He&#x27;s given by sees comments. Ooh, comma zero. 15 Comets in common. Zero and then Sue. Come on 30 And that&#x27;s our answer.

Erin Kirchmeier · Answer

in this problem were given the coordinates of the Vergis ease of a triangle in the coordinate plain. And we are out to find the images of these Vergis ease through this transformation. Remember, this is another way of writing a translation. So what this really means is that each point is not going to move left or right, but they will move up to, according to this translation, Mathematically, what it means is we&#x27;re going to keep the X value of each point. But I had to teach y value. So let&#x27;s get started. So our first vertex is a negative one. Negative one. So under the transformation, I&#x27;m going to keep negative, won the X value and add to to the y value. So the image of this point is negative one one. So our next point 01 under the transformation, we will keep the X value, and we will add to the y value. So I get an image of zero comma three and our last Vertex is that 40 So, under the transformation, I will keep the X, and I will add to to the y value. So our image is that for two. So these are the images of the use of urgencies of the strangle. Under this transformation

Erin Kirchmeier · Answer

in this problem, you&#x27;re given the vergis ease of a triangle in the coordinate plain and were asked to find the images of these points under this transformation. So if you recall, this is another way of writing a translation. So translation means the shape physically moves either up, down, left or right. So under this transformation, the point moves four to the right and one down. So that&#x27;s our translation. However mathematically, how we&#x27;re going to do this is we&#x27;re gonna take each point and we&#x27;re going to add four to the X value and take one away from the Y value. So let&#x27;s get started. Our first point is negative. One negative one. So negative one comma, negative one. We&#x27;re going to take negative won the X value, not forward to it. Then we&#x27;re going to take the Y value negative one and subtract one from it. So this gives us the 0.3 comma negative to as our image of this point, our next point is 01 So we&#x27;re gonna take that and we&#x27;re going to add for two R X value, and we&#x27;re going to subtract one from R A Y value. So this is going to give us the point for zero. And lastly, we ever last point for zero. We&#x27;re going to add for two R X value and we&#x27;re going to subtract one for Mara. Why about you? And this gives us the last point off a negative one. So here are the images of our original points under the given transformation.

Tiffany Tran · Answer

when a I and our eyes drawn, then we create our A.

Gideon Idumah · Answer

Okay, So to answer this question, we states that&#x27;s the metrics off. The transformation that reflects points through the White House is the wife of disease. He&#x27;s a equal to minus 1001 That is, your Tunde. You are a minus one to the ex exist. That is the matrix of transformation that reflects points to the white exists. So this implies that&#x27;s the transformed did some metrics is a mord implied by D because we are told to find the image off the triangle on the the MICEX d. So you do eight times D, which is minus 1001 more supplied by five sue for zero Sue three. Andi transformed mattress These minus 50 minus to do minus four on three. Now we&#x27;re told toe sketchbook. The original triangle on its image says, Dude, that&#x27;s we have something like these. I&#x27;ll just make a sketch here and then we have Let&#x27;s see. 12345 Oh, need one, Sue three. Let&#x27;s end it for So this is X to this is eggs one. So the original image is the original triangle is 5 to 4 sorted there, so I have 50 rights. So that&#x27;s the exes. Five The Y zero. That&#x27;s five. This is one soon 34 fire. So this would be five comma zero. The next one is true. Commit Suso X one is two extras to Dar was somewhere here on the next one is X one is four Extras three. So that&#x27;s four for my three. I was somewhere here and we have this. So this is this. You can just shoot that in Now. The other one is transformed. Image is minus five, comma zero signing to making minus five years. I&#x27;ll be 12345 So I have minus find common zero sadistic beads. X one is minus five. Have minus to commit Su Don&#x27;t be here. And an arm minus four, comma three. So this is minus for under three would be somewhere here. So the image, I guess he&#x27;s This are my over gun sketch this world. Okay, so something like this. So Don sits

Problem

Let $S$ be the triangle with vertices $(9,3,-5),(…

Problem 19 Easy Difficulty

Let $S$ be the triangle with vertices $(4.2,1.2,4),(6,4,2),$ $(2,2,6) .$ Find the image of $S$ under the perspective projection with center of projection at $(0,0,10) .$

Answer

The triangle with vertices $(7,2,0),(7.5,5,0),(5,5,0)$

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

Catherine R.

Kayleah T.

Caleb E.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

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The triangle with vertices $(7,2,0),(7.5,5,0),(5,5,0)$

Linear Algebra and Its Applications

Catherine R.

Kayleah T.

Caleb E.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Catherine R.

Kayleah T.

Caleb E.

Kristen K.

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications