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#1 2015-01-04 04:05:51

Au101
Member
Registered: 2010-12-01
Posts: 353

Parallelograms

Just another one to check whether or not I'm being silly. The question is:

Given that the points A, B, C, D have coordinates (5, 6), (-2, 4), (-5, 5), (2, -3) respectively, prove that ABCD is a parallelogram.

Surely ABCD is not a parallelogram?

I wonder whether the point at (-2, 4) should really be at (-8, -4). (Although, in that case, (-5, 5) should surely be B and (-8, -4) C, if we're going to talk about the parallelogram ABCD.)

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#2 2015-01-04 04:12:07

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Parallelograms

I think C should be (-5,-5).


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#3 2015-01-04 07:08:08

Bob
Administrator
Registered: 2010-06-20
Posts: 10,059

Re: Parallelograms

hi Au101,

Those points do not make a parallelogram.

In general, if 0, P and Q are three distinct points then R = OP + OQ ; OR = OP - OQ ; and OR = OQ - OP all make parallelograms.  Thus there are many ways of changing one point to make a valid question.  I like Stefy's suggestion because it involves a minimal change to the coordinates and thus makes it seem likely that there is a mis-print here.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#4 2015-01-04 07:11:40

Au101
Member
Registered: 2010-12-01
Posts: 353

Re: Parallelograms

Ooooh yes that seems about right, thank you both of you!

So, to prove this, I should presumably show that AB = CD and AD = BC. Should I also show that BD is perpendicular to AC?

Last edited by Au101 (2015-01-04 07:11:58)

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#5 2015-01-04 07:16:11

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Parallelograms

Au101 wrote:

Ooooh yes that seems about right, thank you both of you!

So, to prove this, I should presumably show that AB = CD and AD = BC. Should I also show that BD is perpendicular to AC?

There is no need to show BD is perpendicular to AC. The two equalities are enough.

Weird thing, though - the spellchecker is marking "equalities" in red.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#6 2015-01-04 20:52:28

Bob
Administrator
Registered: 2010-06-20
Posts: 10,059

Re: Parallelograms

hi

'equalities' is correctly spelt.  smile

Or a parallelogram can be proved by opposite sides are parallel.

or one pair of opposite sides are both parallel and equal.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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