Question

What information would you need to find the perimeter of to the right with vertices A(-3,1), B (-1,3) and C(3,1)?

Answer 1

you posted this already. I told you how to do it. why are you reposting?

Answer 2

because i dont understand and still need help im a slow learner especially in math and i need to work it out step by step and not so fast so i can at least understand a little

Answer 3

the ball was in your court to answer...

Answer 4

what

Answer 5

I gave you two subtraction problems. go back and look. http://openstudy.com/users/feedmefoooood#/updates/51dc15b9e4b0d9a104d9c4cb

Answer 6

i dont need to work the problem

Answer 7

i just need information to find the perimeter

Answer 8

to find the perimeter, you need to find the lengths of the sides. to find the lengths of the sides, you need to be able to use the distance formula. to use the distance formula to find the length of the first side, you need to do the subtractions I gave you.

Answer 9

and i did do them

Answer 10

ok you need to chill you are making me frustrated

Answer 11

good. now square both numbers and add them.

Answer 12

("good" responds to "did do them", not "making me frustrated", btw)

Answer 13

they are both 4

Answer 14

okay, add them

Answer 15

8

Answer 16

take the square root

Answer 17

i dont know how to do that without a calculator

Answer 18

can you factor 8?

Answer 19

i dont know what that means

Answer 20

factor means to find the numbers that multiply together to give you that number

is 8 divisible by 2?

Answer 21

yes

Answer 22

okay, so 8 = 2*4, right?

is 4 divisible by 2?

Answer 23

yes

Answer 24

okay, so 8 = 2*2*2, right?

Answer 25

yes

Answer 26

okay. square root means that for every pair of identical factors, we take one away and move the other one of the pair outside the square root sign.

\[8 = \sqrt{2*2*2} = \sqrt{2*2}*\sqrt{2} = 2\sqrt{2}\]
It is generally better to keep it in that form than to convert it to 2.828... while working the problem.

Answer 27

so, we have found the length of 1 of the 3 sides, that from A to B. Now we need to do B to C. Same drill:

B is at (-1,3)
C is at (3,1)

\[(x_1,y_1) = (-1,3)\]\[(x_2,y_2) = (3,1)\]

You need to plug those values into the formula
\[d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\]

This formula is just taking the two sides of the triangles, squaring them, adding them, and taking the square root to find the hypotenuse. Pythagorean theorem.

Answer 28

what is \(x_2-x_1\)?

Answer 29

(3,-1)

Answer 30

no. look at the letters and numbers more carefully.

Answer 31

it's a subtraction, not a point.

Answer 32

4

Answer 33

right!
now what is \(y_2 - y_1\)?

Answer 34

-2

Answer 35

yes.

now look at your picture. look at the triangle formed from the line from B to C, plus a vertical line going down from B, and a horizontal line going from C. Do you see the triangle?

Answer 36

a line cutting it from B?

Answer 37

hang on a minute

Answer 38

triangle formed by the 2 dark red lines plus the line from B to C

Answer 39

ok yes that was what i was saying

Answer 40

okay, that's a right triangle, agreed?

Answer 41

yes

Answer 42

okay, the height of that triangle (the length of the side going from B down toward the x-axis) is how much?

Answer 43

4

Answer 44

look again, I'm talking about the line that goes from B to the spot 2 squares below it.

Answer 45

oh 3

Answer 46

try again. you're getting closer :-)

Answer 47

2??????

Answer 48

yes. and it is no coincidence that \(y_2 - y_1 = 2\)

Answer 49

now look at the bottom of the triangle. how many squares long is it? from the point we were just at (-1,1) over to C (3,1)

Answer 50

4

Answer 51

ill be back in about 20 minutes

Answer 52

very good. again, not a coincidence that \(x_2-x_1\) = 4.

those are the two legs of our right triangle with the line from B to C as the hypotenuse. we square both of the lengths, add them, and take the square root to find the length of the line from B to C.

\[d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} = \sqrt{(3-(-1))^2+(1-3)^2} \]\[\sqrt{ 4^2+(-2)^2} = \sqrt{16+4}= \sqrt{20} \]\[= \sqrt{2*2*5} = \sqrt{2*2}*\sqrt{5} = 2\sqrt{5} \approx 4.472 \]

Now, your job is to find the length of the side from C to A. This one is easier because they are on the same line and you can just count the squares, or subtract the x values — the y values are identical. the distance formula still works, of course, but isn't needed.

when you know how long CA is, add that to your previous two sides, which were

\[AB = 2\sqrt{2} \approx 2.828\]
\[BC = 2\sqrt{5} \approx 4.472\]

and you'll have your perimeter.

Answer 53

ok im backand its 12 right?

Answer 54

no. 12 is neither the length of CA nor the sum of the three sides. how did you get 12?