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A square with area 25 has one vertex on point (-2, 1) in the

Data Sufficiency, Multi-Source Reasoning, Table Analysis, Graphics Interpretation, Two-Part Analysis
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by [email protected] » Sun Jun 22, 2014 4:11 pm
Hi Sri,

This IR question is based on one particular graphing concept: when you draw a diagonal line on a graph, you can draw a right triangle with THAT diagonal line as its hypotenuse.

This prompt tells us that we're dealing with a square that has an area of 25, so it's side lengths all equal 5. With the co-ordinate (-2,1) as a vertex, we're looking for ANOTHER vertex that is "5 away."

The most common triangle on the GMAT with a hypotenuse of 5 is a "3/4/5 right triangle", so I'd be looking for THAT pattern among the answer choices. Is one of the numbers 3 or 4 "away" from -2? Is another 4 or 3 "away" from 1?

"-5" is "3 away" from -2.
"-3" is "4 away from 1.

So, [spoiler](-5,-3) is the vertex.[/spoiler]

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by confused13 » Sun Jun 22, 2014 10:13 pm
This doesn't make sense?

In the (negative, negative) range is only one coordinate (-7,-4) but that's clearly not an option. Could someone explain it in a different way?

The points of the OA and the given point, don't even form a square together?
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by [email protected] » Mon Jun 23, 2014 12:54 am
Hi confused13,

You assume that the square has to be parallel with the X-axis and the Y-axis, but the prompt DID NOT state that. The solution to this question has the square placed "diagonally."

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by confused13 » Mon Jun 23, 2014 3:38 am
So you mean it actually forms an rhombus?
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by [email protected] » Mon Jun 23, 2014 11:07 am
Hi confused13,

It's still a square (it has to be; the prompt says so). To help you visualize what I'm talking about, try drawing a square on a piece of paper. Next, turn the paper a little bit clockwise or counterclockwise. Notice how it's still a square? It's just not "level." This IR question is built on that concept.

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by gmattesttaker2 » Sat Jun 28, 2014 5:39 pm
[email protected] wrote:Hi Sri,

This IR question is based on one particular graphing concept: when you draw a diagonal line on a graph, you can draw a right triangle with THAT diagonal line as its hypotenuse.

This prompt tells us that we're dealing with a square that has an area of 25, so it's side lengths all equal 5. With the co-ordinate (-2,1) as a vertex, we're looking for ANOTHER vertex that is "5 away."

The most common triangle on the GMAT with a hypotenuse of 5 is a "3/4/5 right triangle", so I'd be looking for THAT pattern among the answer choices. Is one of the numbers 3 or 4 "away" from -2? Is another 4 or 3 "away" from 1?

"-5" is "3 away" from -2.
"-3" is "4 away from 1.

So, [spoiler](-5,-3) is the vertex.[/spoiler]

GMAT assassins aren't born, they're made,
Rich
Hello Rich,

Thanks a lot for the explanation. Since the square has an area of 25, its side is 5 and diagonal is 5 sq. root (2). Now, when we join (-5,1) and (-2,-3) we get 3-4-5 triangle. I was wondering though why the diagonal here is 5 and not 5 sq.root(2). Thanks a lot for your help.

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Sri
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by [email protected] » Sat Jun 28, 2014 6:02 pm
Hi Sri,

The side of the square is 5; THAT'S the side that we're interested in (NOT the diagonal of the square).

Try drawing the following points (-5,-3) and (-2,1). If you connect them, then you'll have a diagonal line. Next, using that diagonal line, draw a right triangle. The base will be 3 and the height will be 4; THIS is the 3/4/5 right triangle that I referred to in my explanation.

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