Question

Write a coordinate proof.
If a quadrilateral is a kite, then its diagonals are perpendicular.

Answer 1

@hartnn

Answer 2

Someone please help. This is my last question and I've been working on this for 2 days.

Answer 3

@ayeeturnup

Answer 4

dang im sorry thats harddd

Answer 5

yeah... I've been stuck on it forever and I keep like messaging people and asking them for help but nobody will help...

Answer 6

@hartnn @ganeshie8 can one of you please help me!?

Answer 7

ok so we want to prove that if a quadilateral is a kite, then its diagonals are perpindicular. so we can assume this quadrilateral is a kite. thats the first thing we would do. assume that is given

Answer 8

Okay and then what?

Answer 9

whats the definition of a kite, we will need that

Answer 10

i think in a kite, the two adjacent sides are congruent

Answer 11

A 4-sided flat shape with straight sides that:

* has two pairs of sides.
* each pair is adjacent sides (they meet) that are equal in length.

Also, the angles are equal where the pairs meet.

Diagonals meet at a right angle, and one of the diagonal bisects the other.

Answer 12

@amistre64

Answer 13

lets use this as a template
http://www.algebra.com/algebra/homework/Geometry_proofs.faq.question.555730.html

Answer 14

we can substitute what you have in your drawing

Answer 15

Okay can you show me?

Answer 16

sure

Answer 17

well a coordinate proof is a little different than a geometry proof, since we use coordinates

Answer 18

it would be easier i think to prove it without coordinates,

Answer 19

nah, just show that the slopes of the lines that create the diagonals are perp

Answer 20

ahh, yes that would work

Answer 21

but you have to do it based on whats given

Answer 22

oh nevermind

Answer 23

i was thinking geometry :D

Answer 24

2 points define a slope :) but you might have to use the idea that 1/0 is perp to 0/1

Answer 25

so it looks the proof is 1 line

Answer 26

use pythag thrm otherwise

Answer 27

just use slope formula and youre done?

Answer 28

Okay thanks guys. I get it now. since one slope is undefined and the other is 0 they are perpendicular

Answer 29

ok , slope of diagonal XZ = (b-b)/(2a-0)
slope of diagonal WY = (4b-0)/(a-a)
too easy

Answer 30

correct, as long as you are above to use that definition, then its pretty easy to show

Answer 31

but this doesnt prove that all kites have diagonals that are perpindicular

Answer 32

this only proves that the given figure has diagonals perpindicular

Answer 33

the given is a kite;

Answer 34

it says if its a kite, then ______

we have a kite, show that its perped

Answer 35

the statement reads
"if a quadrilateral is a kite, then the diagonals are perpindicular".
this is a special case of a kite, draw in the figure

Answer 36

the figure is a generality of a kite, which is why there are no specific point values

Answer 37

well i think a proper proof would say that any kite can be drawn like this.

Answer 38

All kites can be construced as WXYZ, the ab parts make it so that you can define ANY kite by this general construction

Answer 39

i dont see anywhere in the directions where it says this figure is a kite.
what i would do first is show that it is a kite, by proving the adjcent sides are congruent

Answer 40

so you can use pythagorean theorem, to show that WZ = WX , and the other two sides are congruent.

Answer 41

the hypothesis does not have to be demonstrated. It only has to be generalized to fit ANY construction that matches the definition of a kite.

Answer 42

and the last step can be, since any kite can be drawn like the kite in the diagram (by rotation, scaling, whatever), and since we proved the slopes are perpindicular, then we are done

Answer 43

right, but what if you drew a non-kite and then proved its diagonals are perpindicular (which happened to be a coincidence). i mean, its good to just check that it is in fact a kite.

Answer 44

for me the proof to be persuasive is that the figure is actually a kite. i dont trust somebody just drawing something freehand

Answer 45

and then say, oh my freehand drawn kite has diagonals perpindicular.

Answer 46

if p then q = -p v q

p -p q -pvq
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 1 <-- this setup is what we are going for.


if p is false, then q is true regardless

we are assuming that p is given, and is true
show that q is true to verify the statement
or show that q is false to contradict the statement

Answer 47

but its pretty easy to check by pythagorean that the sides are congruent. im just saying that it is a good step. even if the directions say, this figure is given as a kite, I think the coordinates of the kite should reflect that. what if there was a typo in the figure, you know. its just one extra step.

Answer 48

lol, um, if p is false, then the statement is true regardless of q is what i should have said ...

Answer 49

right, but then you are not proving the claim that all kites have perpindicular diagonals. since you did not draw a proper kite in the first place

Answer 50

im not opposed to verifying the kiteness of it :)

Answer 51

my point is, if they happened to draw a non kite, then you didnt prove the claim that all kites have perpindicular diagonals, even if the figure turned out to have perpindicular diagonals (or not).

Answer 52

i understand that we want to look only at kites, since it is trivially true for non kites. thats my point. how do we know its a kite. you say its given, ok, let me check the coordinates on this 'given' kite

Answer 53

i guess what im saying is, if you wanted to prove this from scratch, then you should justify that your given kite is really a kite, since we are using coordinates.

Answer 54

ok consider this scenario.
Suppose you wanted to do a proof from scratch let say, and by accident you draw a non kite on the coordinate plane and then by coincidence the diagonals are perpindicular. and you think you have proven the claim.