Alan G. answered • 03/02/16

Successful at helping students improve in math!

_{2}- x

_{1})

^{2}+ (y

_{2}- y

_{1})

^{2}]

Claudia C.

asked • 03/02/16D(0,1),E(5,4) and F(2,6)

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Alan G. answered • 03/02/16

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Since three vertices are given, the figure must be a triangle. To find the perimeter, you must find the lengths of all three sides and add them up. The lengths can be found using the distance formula:

d = √[(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}]

The lengths of the three sides using this formula are:

DE = √34

EF = √13

DF = √34 .

Thus, the perimeter is P = 2√34 + √13 . Notice that the triangle is isosceles since two of the sides have equal lengths.

If you need a decimal answer, you should use a calculator.

Marina B. answered • 03/02/16

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Dear Claudia,

Let me get you started on this. Vertices are just corners, and because there are only three points, you can be sure it's a triangle. We know that a perimeter is the sum of the lengths of all the sides. There are three. How can you find side lengths? Do you remember the distance formula? (Hint: the distance formula for length between two coordinate points.)

- apply it to points D & E = side one
- then same for D & F = side two
- then lastly for E & F =side three
- add all your results for the three sides => perimeter!

It sounded trickier than it was, but this problem is a lot of work with a lot of calculations. Hope this helps. Let me know if you need to see a calculation of one of the sides.

~Best,

Marina

Marina B.

If you have the points correctly, then I also got square root of 29 for DF:

D(0,1) and F(2,6)

d = √[(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}]

d = √[(2 - 0)^{2} + (6 - 1)^{2}] = √[(2)^{2} + (5)^{2}] = √[4+ 25] = √[29]

d = √[(x

d = √[(2 - 0)

Does the back of the book say it's √[34]?

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03/03/16

Claudia C.

No two people answered my questioned and other person said it was an isosceles triangle, but I must have done it right and he did it wrong. Thank you so much for verifying for me.

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03/03/16

Marina B.

Okay, Claudia, small mistakes happen to everyone ;) especially if we try to do it in our heads. You are welcome.

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03/03/16

Alan G.

Thanks for the clarification. I was mistaken about the triangle being isosceles. Marina is correct about the side DF being equal to √29. My fault was (as she said) that I did this in my head and was tired at the time.

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03/03/16

Marina B.

I guess the lesson here is (and it's a very good lesson) in a test situation *write down all your steps/work. *It will be easier to track down any mistakes later. Otherwise, you can lose points for human error. The other being, have confidence in your work if you see you have followed the "recipe" of the formula correctly.

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03/03/16

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Claudia C.

03/03/16