Question

LAST ONE:
A retention pond is located close to a sidewalk where small children play. The city plans to fence it in to keep children from accessing the water. What is the perimeter of a triangular-shaped fence the city can place around the retention pond, using integer coordinates (no decimals) on the grid? You must show all work to receive credit.

Answer 1

Last one @ganeshie8

Answer 2

So I will need to draw the triangle, just barely touching the edge of the pond. Put the vertices at points A,B,C, then find distances AB AC BC and add them to get perimeter total length.

Answer 3

Then to get the perimeter, all the 3 lines length, using the "distance formula"
D = {x*2 - x*1} *2 + { y*2 - y*1} *2

Answer 4

Dont know the rest :\

Answer 5

You have everything u need :)

Answer 6

start by *deciding* the vertex points of triangle

Answer 7

Keep in mind - you need to pick vertex points such that the pond lies completely inside the triangle

Answer 8

Thats pretty diffcult

Answer 9

yeah lets try

Answer 10

ok

Answer 11

Ok so im pretty bad at this but the start point of the tringle would be -4,6 I think?

Answer 12

see if that triangle works ^

Answer 13

That looks much better ^^

Answer 14

Ok so now what @ganeshie8

Answer 15

find the length of each side

Answer 16

Look at the triangle - can you tell the coordinates of vertices ?
A = ?
B = ?
C = ?

Answer 17

A = -4,5
B = 2,5
C = -9,4
This is supposing I did it in the correct order :)

Answer 18

order doesn't matter, so you're right !
but check the numbers again :)

Answer 19

Opps C = -9, 5 My bad

Answer 20

you should get :

A = (-4, -5)
B = (2, 5)
C = (-9, 5)

Answer 21

Yes !

Answer 22

next, find the lengths of AB, BC and CA using distance formula

Answer 23

So d = {-5 - -4}*2 + {5 - 2}*2

Answer 24

square root is missing ^

Answer 25

d = -9*2 + 3*2
d = -18 + 6 = -12

Answer 26

Opps i do square root like this *

Answer 27

leme show u calculating the length of side AB :

A = (-4, -5)
B = (2, 5)

Answer 28

Ok

Answer 29

length of side AB = \(\sqrt{(5--5)^2 + (2--4)^2} = \sqrt{(10)^2 + (6)^2} \\ =\sqrt{100 + 36} = \sqrt{136} \)

Answer 30

OMG RIGHT! im so sorry its supposed to be x -x and y - y SORRY!

Answer 31

You got it !
try finding BC :)

Answer 32

d = {5 - 5)*2 + (-9 - 2)*2
d = 0*2 + -11*2
d = 0 + -22
d = -22

Answer 33

Ok is that correct

Answer 34

Good try ! but no... the distance can never be negative okay ?

Answer 35

B = (2, 5)
C = (-9, 5)

length of side BC = \(\sqrt{(-9-2)^2 + (5-5)^2} = \sqrt{(-11)^2 + (0)^2} \\ =\sqrt{121} = 11 \)

Answer 36

d = ( 5 - -5)*2 + (-9 - -4)*2
d = -10*2 + 13*2
d = 100 + 169
d = 269 Ok this better be correct :)

Answer 37

d = 16

Answer 38

slight mistake :P

Answer 39

in first line

Answer 40

whats the value of -9--4 ?

Answer 41

5

Answer 42

Yes, -9--4 = -9+4 = -5

Answer 43

So whats the distance of CA ?

Answer 44

So then 125 = 5

Answer 45

C = (-9, 5)
A = (-4, -5)

length of CA = \(\sqrt{(-4--9)^2 + (-5--5)^2} = \sqrt{(5)^2 + (10)^2} \\ =\sqrt{125} \)

Answer 46

add all the side lengths to get the perimeter

Answer 47

perimeter of triangle = AB + BC + CA
= \(\large \sqrt{136} + 11+ \sqrt{125}\)

Answer 48

use ur calculator

Answer 49

Ok

Answer 50

http://www.wolframalpha.com/input/?i=+%5Csqrt%7B136%7D+%2B+11%2B+%5Csqrt%7B125%7D

Answer 51

So pretty much decimal output would be 33.84

Answer 52

Would that be it @ganeshie8

Answer 53

33.84

Answer 54

thats it !

Answer 55

YAY! THANK YOU SOOOOOOO MUCH UR THE BEST TEACHER EVER :)

Answer 56

np :D

Answer 57

nice problem