Math Is Fun Forum

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.)

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Parallelograms

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

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“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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

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

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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

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)

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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?

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.

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“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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Parallelograms

hi

'equalities' is correctly spelt. 

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

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

Bob

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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