SURD QUESTION-ADVANCED mathematicians...PLEASE heelpp..?

Question

The Question is--

A square has vertices with the coordinates (2,1) , (4,2) , (5,0) and (3,-1)

Show that the perimeter of this square is 4(square-root)5.

How would i work this out, please use as much detail so i can understand!! Go through STEP by step it may take a long time, but you are helping me AND you WIll WIN 13 points total for your efforts.

SPREAD THE KNOWLEDGE-- PLEASE!!!!!!

thanks.

Answer 1

Plot the 4 points

Confirm which segments are Sides and which Diagonals

Recall distance between P1 (x1, y1) and P2 (x2, y2) = SquareRoot [(x2-x1)^2 + (y2-y1)^2]

Any of the 4 sides gives you length of Root 5

So PERIMETER = 4 Root 5

Answer 2

Ok

-determine which two points make a side not a diagonal (make a quick sketch)

-find the length of one side......

   distance formula

          d=sqrt[(x2-x1)^2 + (y2-y1)^2]

            =sqrt[(4-2)^2 + (2-1)^2]

            =sqrt(5)

- there are 4 sides to a square so..........

       perimiter= 4xsqrt(5)

Answer 3

Let  the points be –

A ( 2, 1 ) ,  B ( 4, 2 ) , C ( 5, 0 ) and D ( 3, -1 )

If we joint any two points, it may either be a side or a diagonal

of the square. At the same time we know that the square has

all the sides equal to each other.  So our effort will be to find out

FOUR equal sides and then add them up to get the perimeter.



We know that if (x1,y1)  and (x2,y2) are two points,

then the distance between these points is ----------

(x2 - x1)² + (y2 - y1)² . Applying this formula we get----

AB  =  ÃƒÂ¢Ã‚ˆÂš[  (2-4)^2  +  (1-2)^2 ]  =  ÃƒÂ¢Ã‚ˆÂš5

AC  =  ÃƒÂ¢Ã‚ˆÂš[  (2-5)^2  +  ( 1-0)^2 ]  =  ÃƒÂ¢Ã‚ˆÂš10

AD  =  ÃƒÂ¢Ã‚ˆÂš[ (2-3)^2  +  (1 + 1)^2 ]  = √5

Here it is clear that the measure of each side is = √5,

and its diagonal is  ÃƒÂ¢Ã‚ˆÂš10 units long.

Hence Perimeter =  ÃƒÂ¢Ã‚ˆÂš5   +   √5  +    ÃƒÂ¢Ã‚ˆÂš5   +   √5     =  4√5  ÃƒÂ¢Ã‚€Â¦Ã¢Â€Â¦Ã¢Â€Â¦Ã¢Â€Â¦..  Answer  

Dr. P.K.Tandon

Answer 4

The formula to work out the distance of a line is:

(x2 - x1)² + (y2 - y1)² = distance²

(The 1s and 2s in front of the letters should be in subscript)

So now we can plug the values in for these.

So:

(4-2)² + (2-1)² = D²

4 + 1 = D²

D = √5

And there are 4 sides to a square, so we multiply √5 by 4 to get 4√5.