June 2007 Regents Question 33

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Polishgirl

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I need help solving this particular math problem from the June 2007 Regents Examination

Given: quadrilateral ABCD with vertices A(-2,2), B (8,-4), C(6,-1O) and D ( -4,-4). State the coordinates of A'B'C'D' the image of quadrilateral ABCD under a dilation factor of 1/2.
Prove that A'B'C'D' is a parallelogram.
 
Polishgirl said:
I need help solving this particular math problem from the June 2007 Regents Examination
Given: quadrilateral ABCD with vertices A(-2,2), B (8,-4), C(6,-1O) and D ( -4,-4). State the coordinates of A'B'C'D' the image of quadrilateral ABCD under a dilation factor of 1/2.
Prove that A'B'C'D' is a parallelogram.
Click to expand...
You know that \(\displaystyle OP'=\frac{1}{2}OP\).
Now prove that \(\displaystyle |A'B'|=|C'D'|~\&~AB||CD\).
 
Polishgirl said:
I can not prove anything
Click to expand...

First things first. Before proving anything, this exercise asks you to find the coordinates for points A', B', C', and D'.

Can you do this?

I mean, seriously, if a person does not understand phrases like "image of quadrilateral ABCD" and "dilation factor of 1/2", how could this person possibly prove (let alone understand) anything in this exercise?

The proof that I'm thinking of requires the coordinates for points A', B', C', and D'. It involves using these coordinates in the distance formula twice, to show that the length of side A'B' is equal to the length of side C'D'. It involves using these coordinates in the slope formula twice, as well, to show that the slope of side A'D' equals the slope of side B'C'.

You need to know what defines a parallelogram, too, to understand this approach to the proof. Do you know what a parallelogram is?

Can you use the distance formula, given the endpoint coordinates of a line segment?

Can you use the slope formula, given the same coordinates? (Do you know what "slope" means?)

If your answer to any of my questions (in this post) is "no", then that's where you should start.

Let us know WHY you're stuck and what you already know about this stuff.

I'm willing to guide you through it, if I see you make an effort. Be forewarned, though; if it turns out that you have no pre-requisite knowledge of the concepts involved here, you and I will be exchanging about a dozen posts each.

Cheers ~ Mark 8-)
 
Just because Im not able to solve this particular problem doesn't mean I don't know anything. I'm a senior in a high school, and I'm definately not slow. If I wouldn't have to do this project for school , I wouldn't even write on this message board. I would just ask my parent.


Of course I know what a parallelogram is , I know how to use distance and I know what slope is

Sorry if I'm a little rude, I just don't like to be put down.
ok, so please help me solve this , I don't have forever, i don't sit on the computer 24/7


should I graph it? or what?
 
You need to check out the post titled, "Read before posting".

With all of your knowledge, you're old enough to form specific questions, yes?

In other words, the way it works here is (1) you show us what you can do, and (2) we help you along. This board is not an on-line classroom.

What did you get for the coordinates of points A', B', C', and D' ?
 
Polishgirl said:
should I graph it? or what?
Click to expand...

If you find graphic aids to be helpful, then sure, a rough sketch would be a very good :idea: .

Maybe then you'll "see" that side A'B' must be the same length as side D'C' (as pka already told us) per the parallelogram definition that you know, and that the slope of side A'D' must equal the slope of side B'C' (as pka already told us) per the parallelogram definition that you know.

Since you continue to avoid direct questions, I've found that you're disinterested in every approach save spoonfeeding.

Please come back, when you find some motivation to respond.
 
haha its ok. i got it solved already..

you can go live your life now. never mind me.

bye.
 
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