Question

Guys I need help with a problem. I have the first half figured out...

Determine if triangle DEF with coordinates D (2, 1), E (3, 5), and F (6, 2) 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

Well first off, We know that an equalaterial triangle has to be equal in length. SO I found the lengths of the sides. DE=17squared EF=18squared FD=17squared so at this moment its an isosceles not equal. When you move a point, it changes the length of two sides, not just one....

Answer 1

using trig?

Answer 2

Did you mean

\[\Large DE = \sqrt{17}\]

\[\Large EF = \sqrt{18}\]

\[\Large FD = \sqrt{17}\]

??

Answer 3

yes

Answer 4

But I need help

Answer 5

sorry

Answer 6

ok one second while I think over how to solve

Answer 7

are you able to graph each point on the xy coordinate system?

Answer 8

yes

Answer 9

what graphing tools do you have?

Answer 10

microsoft paint

Answer 11

I can make graphs

Answer 12

have you heard of geogebra?

Answer 13

yes

Answer 14

I'm using that program and it's highly more accurate

Answer 15

so go ahead and download and install that (it's a free program)

Answer 16

ok I can use geogebra

Answer 17

now what

Answer 18

is the program running?

Answer 19

yes

Answer 20

ok do you see the "input bar" at the bottom?

Answer 21

yes

Answer 22

type in D = (2, 1), then hit enter, to plot the point D

Answer 23

do the same for the other 2 points

Answer 24

tell me when you have done that

Answer 25

ok

Answer 26

yes

Answer 27

at the top, you should see this icon

http://wiki.geogebra.org/uploads/1/1e/Tool_Circle_Center_Point.gif

Answer 28

do you see it?

Answer 29

so its equalaterial im not sure I can see it

Answer 30

it looks equilateral, but you've proven above that it is not equilateral

Answer 31

do you see that icon?

Answer 32

yeah

Answer 33

in the corner

Answer 34

click that icon. Then click on point D. And then click on point E

You should see a circle pop up (centered at D and going through point E)

Answer 35

Nothing is happening]

Answer 36

can you explain to me what im supposed to be seeing

Answer 37

one sec

Answer 38

ok here are the three points D, E, F (see attached)

Answer 39

Draw a circle that is centered at point D that goes through point E

Answer 40

Notice how F is also on that circle. So this proves (at least visually) that DE = DF

You've shown above that they are indeed equal because they both equal \(\Large \sqrt{17}\)

Answer 41

Now draw a circle centered at point E and that goes through point D

This circle will have the same radius as the last circle

Answer 42

I can clearly see now that it is Isoseles

Answer 43

notice how point F is NOT on the circle we just drew

so this triangle is isosceles, but not equilateral

Answer 44

to fix that, move point F to either point of intersection between the two circles

Answer 45

now we have to make it equalaterial

Answer 46

so move point F (in blue) to either point G (in red) or point H (in red)

Answer 47

to analytically find those points G and H, you need to solve the system of equations

(x - 2)^2 + (y - 1)^2 = 17
(x - 3)^2 + (y - 5)^2 = 17

Answer 48

ok