Math Is Fun Forum

ilovealgebra

Member

Registered: 2006-10-02

Posts: 40

coordinate geometry

A(7,2) and C(1,4) are two vertices of a square ABCD

(a) Find the equation of the diagonal BD.
(b) Find the coordinates of B and D.

I have answered (a), but i cant seem to get (b), can someone please show me how to get (b). thanks=)

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"...nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called into question (much less condemned) upon the testimony of biblical passages."
-Galileo Galilei

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: coordinate geometry

A = (7,2)
C = (1,4)

im not sure how you are meant to work it out. but taking the midpoint of AC = (4,3). take the vector from the midpoint to A and you have (3,-1). which if you rotate 90 degrees anticlockwise is (1,3). which if you add onto midpoint gives you B or D whichever way you want to have the vertices ordered, and subtracting from midpoint will give the other point.

i.e. (4,3)+(1,3) = (5,6) lets say this is B
(4,3)-(1,3) = (3,0) lets say this is D

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The Beginning Of All Things To End.
The End Of All Things To Come.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: coordinate geometry

....x..6
.......5
x......4
...c...3
......x2
.......1
..x....0
1234567

I can see it right because
I have a fixed space font
over-ride option in my
browser.

Last edited by John E. Franklin (2008-03-13 10:45:16)

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igloo myrtilles fourmis

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: coordinate geometry

Putting things in code is a good way of making sure you get uniform spacing.

....x..6
.......5
x......4
...c...3
......x2
.......1
..x....0
1234567

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Why did the vector cross the road?
It wanted to be normal.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: coordinate geometry

too bad the x/y scale is still off

6 . . . . . B . . 
5 . . . . . . . .  
4 . C . . . . . . 
3 . . . . M . . . 
2 . . . . . . . A 
1 . . . . . . . . 
0 . . . D . . . . 
. 0 1 2 3 4 5 6 7

Last edited by luca-deltodesco (2008-03-13 10:58:04)

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The Beginning Of All Things To End.
The End Of All Things To Come.

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: coordinate geometry

I did it a little different but you get same result.

First of all I found the distance between A and C to be:

so since this is the diagonal it means that:

Since this is a square then BC and BA have to be of same length so we let u = BC = BA so it becomes

So you know that the length of the sides of the square are sqrt(20). In this way you could find points B and D knowing the distance from A and C is sqrt(20) etc....I guess I overcomplicated this but thats how I got it.

Last edited by LuisRodg (2008-03-13 11:10:16)