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anonymous
 one year ago
Determine if triangle DEF with coordinates D (3, 2), E (4, 6), and F (7, 3) is an equilateral triangle. Use evidence to support your claim. If it is not an equilateral triangle, what changes can be made to make it equilateral? Be specific.
anonymous
 one year ago
Determine if triangle DEF with coordinates D (3, 2), E (4, 6), and F (7, 3) is an equilateral triangle. Use evidence to support your claim. If it is not an equilateral triangle, what changes can be made to make it equilateral? Be specific.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I used the distance formula for each segment in triangle DEF and have come to the conclusion that the triangle is not an equilateral triangle. The distance for Segments DE and DF are sq.rt.17, but the distance for Segment EF is sq.rt. 18. I am having difficulty answering the second part of the question, "If it is not an equilateral triangle, what changes can be made to make it equilateral? Be specific." Please provide guidance as to how to go about answering this question. Thank you!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Find the distance between D and E to determine the length of Segment DE. D = (3,2) and E = (4,6) Step 1: d = sq.rt. (x2  x1)^2 + (y2  y1)^2 Step 2: d = sq.rt. (4  3)^2 + (6  2)^2 Step 3: d = sq.rt. (1)^2 + (4)^2 Step 4: d = sq.rt. 1 + 16 Step 5: d = sq.rt. 17 Find the distance between E and F to determine the length of Segment EF. E = (4,6) and F = (7,3) Step 1: d = sq.rt. (x2  x1)^2 + (y2  y1)^2 Step 2: d = sq.rt. (7  4)^2 + (3  6)^2 Step 3: d = sq.rt. (3)^2 + (3)^2 Step 4: d = sq.rt. 9 + 9 Step 5: d = sq.rt. 18 Find the distance between D and F to determine the length of Segment DF. Step 1: d = sq.rt. (x2  x1)^2 + (y2  y1)^2 Step 2: d = sq.rt. (7  3)^2 + (3  2)^2 Step 3: d = sq.rt. (4)^2 + (1)^2 Step 4: d = sq.rt 16 + 1 Step 5: d = sq.rt. 17

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1i guess, sqrt(18)  sqrt(17) needs to be taken off EF, and recalculate the position of one of the points

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I agree, but I have tried different combinations and have failed to find an alternative point.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1By distance formula , you have \(EF =\sqrt{(74)^2+(36)^2}=\sqrt {18}\) Only one way you can do is to make it down to \(\sqrt{17}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That is what I thought before, but I got points off because I didn't give an alternative point.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1by changing the location of E. F cannot be changed because it relates to D

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1if E( 6, 7) then you get the required triangle.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Read the problem, they say : by what changes??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, thank you so much!

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1my change is the point E from (4, 6) to (6,7)

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1E or F can move in a circle around point D, right

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1@DanJS It is a good idea but I don't think they use the orbit concept here.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I plugged in 6,7 yet still got different measures for each distance. Did I do something wrong?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1oh, yea!! I am wrong!!

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1since if you change E, then DE changes also. OMG. I am terribly sorry.

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1I dont see how that has to happen, if you move E , DE can stay the same length, the radius of the circle, when you move E on an Arc towards F

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1or F towards E the same way

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1I know how to do!! Thanks God. He gives me a chance to fix my mistake. hehehe.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Lol thank you both for your help and patience!

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1Circle centered at D, radius root(17), you just swing F towards E or E towards F, till the chord EF is root17

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1or set up two distance formula , and use (x,y) for F, and figure out x and y, possibly

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I tried your second option, but every time I changed a coordinate, I failed to get the same measure for each segment.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1\(DE=\sqrt{(x_E3)^2+(y_E2)^2)}\) \(EF=\sqrt{(7x_E)^2+(3y_E)^2)}\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1and we want DE = EF, so, solve for it!!

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1\(DE = EF = \sqrt{17}\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1ok, take over, please. hehehe.. I tried to fix my mistake but if you know how to do, please, finish the stuff. I am not good at explaining. Please :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the change or different coordinate is (x,y)?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1there are two possible points for F, one on each side of the Y axis, i think

DanJS
 one year ago
Best ResponseYou've already chosen the best response.117 = (x4)^2 + (y6)^2 17 = (x3)^2 + (y2)^2 i solved those with a computer,

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So D still equals (3,2)...E still equals (4,6). What does F = ?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1\[F(x,y) = (\frac{ 4\sqrt{3} + 7 }{ 2 } , \frac{ 8\sqrt{3} }{ 2 }) \approx (6.9641, 3.1340)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Woah...that is very precise. I think I may have gone about answering this question the wrong way because I doubt my teacher would have expected such an answer.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you think I should answer using your original suggestion, "i guess, sqrt(18)  sqrt(17) needs to be taken off EF, and recalculate the position of one of the points,"....?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1\[FD = FE = \sqrt{17}\] that what those 2 distance equations above are

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you for your help and time! If you could, would you please help me formulate my final answer. If not, I totally understand because I have already taken up so much of your time!!

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1then maybe, move F up a little, and relable that F' point (x,y), EF' = root (17) to make an equilateral triangle

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, that is perfect! Thanks again. Can I give you multiple awards...other than just a medal?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1only things i know are fan and testimonial

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1@Loser66 did just as much...

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1hover over name, and buttons are there

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, I gave you a medal, became a fan and submitted a testimonial. Thanks!!

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1hah, thanks, ill fan you to

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No need!! Good night!!
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