• Support PF! Buy your school textbooks, materials and every day products Here!

Coordinate geometry

  • Thread starter denian
  • Start date
  • #1
160
0
just wanna ask a simple question

a quadrilateral has the vertices A ( 1,4 ), B (9,5 ) , C ( 5,-2) and D (-3,-3). show that the quadrilateral is a rhombus

what i do is find gradient AB, CD, AD and BC.
and then state which and which have the same gradient... and hence the opposite sides are parallel.

is that all i should do?
 

Answers and Replies

  • #2
AKG
Science Advisor
Homework Helper
2,565
3
Unless they're doing something tricky, the sides should be AB, BC, DC, and AD. Show that AB = DC, BC = AD, and |AB| = |BC|, and you're done. Basically a rhombus as two defining properties:

1) all four sides have the same length
2) opposite sides are parallel

In truth, it's sufficient to simply show that all four sides have the same length, and property 2 will follow, so that's one alternative approach. I would say try both, and see which one feels easier/more efficient. As for your approach, I don't know what you mean by gradient, so I can't say whether it will work or not.
 
  • #3
1,789
4
The two sufficient conditions to prove are:

1. All 4 sides are equal (opposite sides are parallel).
2. The diagonals are not equal.

AKG: By gradient, denian means slope of a line joining [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] defined as:

[tex]
m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}
[/tex]

Cheers
Vivek
 
  • #4
160
0
thank you!
 

Related Threads for: Coordinate geometry

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
12
Views
4K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
2
Views
12K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
1K
Top