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In the x-y plane, the coordinates of three consecutive

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In the x-y plane, the coordinates of three consecutive

by BTGmoderatorLU » Tue Jun 05, 2018 3:09 pm

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In the x-y plane, the coordinates of three consecutive vertices of a rectangle are (2a, b), (-2a, b), (-2a, -3b). If a and b are integers with a<0 y b >0. Which of the following could be the coordinates of the fourth vertex?

A. (-3, -2)
B. (-2, 3)
C. (6, -9)
D. (-6, -9)
E. (-6, 9)

The OA is D.

Both B and D are possible.

For B, a = -1, b = 1
(-2,1), (2,1), (2,-3), and (-2,-3) for the coordinate (2a, -3b)(a square is a rectangle)

For D, a = -3, b = 3

Are the answer choices correct? Or am I missing something really obvious? Can anyone assist me please? Thanks in advance!
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by [email protected] » Tue Jun 05, 2018 9:21 pm
Hi BTGmoderatorLU,

We're told that in the x-y plane, the coordinates of three consecutive vertices of a rectangle are (2A, B), (-2A, B), (-2A, -3B), A and B are both INTEGERS with A < 0 and B > 0. We're asked which of the following COULD be the coordinates of the fourth vertex? TESTing VALUES is a great approach for this prompt, but you made a small error in one of your calculations.

In your example, A = -1, B = 1, the three given co-ordinates would be (-2, 1), (2, 1), and (2, -3), so the missing coordinate would need to be (-2, -3). That is NOT what's stated in Answer B. Your work for Answer D is correct.

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by nidhips » Wed Jun 13, 2018 9:03 pm
how do you choose the values for a and b?
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by [email protected] » Thu Jun 14, 2018 5:59 pm
Hi nidhips,

To start, you should notice that the questions asks what "could" be the co-ordinate (not "what is" the co-ordinate). This means that there will almost certainly be multiple correct answers to this question - but only one of the 5 given answers is correct.

If you are just learning to TEST VALUES (re: choose numbers), then we're going to start with a simple example for this question. We're told that A and B are both INTEGERS; A is negative and B is positive. Try this:
1) Choose a couple of simple numbers for A and B (keep them small though; you're going to do some graphing in a minute).
2) Using the A and B that you chose, graph the 3 co-ordinates that are described.
3) You will now have the 3 'corners' of a rectangle. Using your graph, where would the 4th co-orindate be?

If you're comfortable with what you just did here, then you can now use the answer choices to your advantage.... Based on how the answer choices are written, and the work that you already did, you know that you will end up multiplying A by 2 or -2 and you'll be multiplying B (at certain points) by -3. Answers C, D and E certainly fit the type of 'pattern' that the 3 given co-ordinates 'hint at', so A is probably meant to be 3 or -3 and B is meant to be 3 or -3. Remember that the prompt tells us that A is NEGATIVE and B is POSITIVE, so that should make choosing A and B a lot easier.

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