Question

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?

Answer 1

Do you know the distance formula for the distance between two points \((x_1,y_1),(x_2,y_2)\)?

\[d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\]

what do you know about the lengths of the sides of an equilateral triangle?

Answer 2

They all must be equal..

Answer 3

I used GeoGebra and saw that it isn't a equilateral triangle

Answer 4

Just having trouble of how to make it a equilateral triangle

Answer 5

Okay, are two of the sides equal in length?

Answer 6

Yes.

Answer 7

Still there? @whpalmer4

Answer 8

well, then take a point which isn't equidistant from two of the other points, and move it so that it is :-)

Answer 9

can you give me an example?

Answer 10

okay, what is the length of the side that is equal for two sides?

Answer 11

4.12

Answer 12

no, it's not. it might be a number close to that. stick to exact numbers, which means if you have a square root that you can't simplify, write \(\sqrt{17}\) (or whatever) instead.

Answer 13

in fact, you're usually best off avoiding decimals entirely until you have the final answer, and even then, use a decimal only if the problem asks for one.

Answer 14

Okay, so your problem is to find a point which is \(\sqrt{17}\) away from two of the other points (which are \(\sqrt{17}\) apart from each other).

Answer 15

You can do this with the distance formula (which is really the Pythagorean theorem in disguise).

What are the two points which are \(\sqrt{17}\) apart and that you will keep for your new triangle?

Answer 16

i honestly don't know..

Answer 17

you told me you found the distance between the points. did you, or didn't you?

Answer 18

you have 3 points. 2 pairs of those points are sqrt(17) apart. 1 pair is not. pick one of the pairs that is, and tell me what the points are.

Answer 19

(3,2)

Answer 20

okay, now give me one of the other pairs, which is sqrt(17) away from (3,2)

Answer 21

(4,6)

Answer 22

Here's a question for you: do you think the problem is asking for you to find the exact points to use to make this an equilateral triangle, or just describe in general terms how to make an equilateral triangle?

Answer 23

I already have the exacts points etc. i just need to find out points that do make a equilateral triangle..

Answer 24

you have the exact points to make this an equilateral triangle? how do you know that without knowing what your equilateral triangle is?

Answer 25

I'm trying to figure out how to create a equilateral triangle

Answer 26

since coordinates D (3, 2), E (4, 6), and F (7, 3) is not q equilateral triangle
i must find points that do make one

Answer 27

@sourwing