Question

already got help :]

Answer 1

your setup is fine, you have used the distance formula correctly.

Answer 2

now the thought is, which point do you want to move?

Answer 3

does moving 1 point change 2 sides? or does it only affect one side?

Answer 4

It changes two sides?

Answer 5

yeah, so what I would do, to make life simple, is change the point in common to the equal length sides. to get them to match the 3rd side

Answer 6

DE and DF are the same length, they have the point D in common

let move it so that the distance from D to F, and D to E is the same is the other side.

or this can be done with any of the point, i just picked one that seemed simple

Answer 7

thats one approach yes

let D = (x,y) and we can then determine its required values

Answer 8

\[d^2 = 18 = (x-4)^2 + (y-6)^2\]
\[d^2 = 18 = (x-7)^2 + (y-3)^2\]

\[ (x-4)^2 + (y-6)^2 = (x-7)^2 + (y-3)^2\]

\[ (x-4)^2 + (y-6)^2 = ((x-4)-3)^2 + ((y-6)+3)^2\]
\[ (x-4)^2 + (y-6)^2 = (x-4)^2+9-6(x-4) + (y-6)^2+9+6(y-6)\]
\[ (y-6)^2 = 9-6(x-4) + (y-6)^2+9+6(y-6)\]
\[ 0 = 18-6(x-4)+6(y-6)\]
\[ 0 = 3-(x-4)+(y-6)\]
\[ (y-6) = (x-4)-3\]
\[ y= x-1\]

Answer 9

give me a sec to review this.

Answer 10

we know what y needs to be, its 1 less then x

lets solve for x

18 = (x-4)^2 + (y-6)^2

18 = (x-4)^2 + (x-1-6)^2

can you work a quadratic? or do you think theres a simpler way?

Answer 11

heheh, or we can move all the points

Answer 12

if we adjust ALL the points, we dont even need to be confined to sqrt(18)

we have total freedom!!

Answer 13

so its up to you how you want to proceed really

Answer 14

by pythag we can determine the height of a equilateral triangle


E(0,0) F(2,0) D(1,sqrt(3))