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What are the coordinates of point B ?

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Source: — Data Sufficiency |

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by [email protected] » Sat Sep 20, 2014 10:51 am
HI gmat_guy666,

If the picture that you attached is part of the original question, then you can solve this DS prompt with very little actual "math" work (as long as you recognize what you're looking at).

Here, we have a RIGHT TRIANGLE, which means that we can use Right Triangle "rules" to our advantage. We have the length of 1 of the 3 sides, so if we're given the length of either of the other 2 sides, then we COULD figure out the length of the 3rd side and the co-ordinate of Point B.

Fact 1: Area of the triangle = 30.

Since we already have the "height" of the triangle, we can use the Area Formula [(1/2)(B)(H) = 30] to figure out the "base" - with THAT length, we COULD determine the co-ordinate of Point B.
Fact 1 is SUFFICIENT

Fact 2: Line segment CB = 13.

This gives us the diagonal of the right triangle. We can now use the Pythagorean Theorem (A^2 + B^2 = C^2) to figure out the length of the "base" - and just as in Fact 1 (above) we COULD determine the co-ordinate of Point B.
Fact 2 is SUFFICIENT

Final Answer: D

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Rich
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What are the coordinates of point B ?

by Brent@GMATPrepNow » Sat Sep 20, 2014 1:24 pm
gmat_guy666 wrote: Image
What are the coordinates of point B ?

1) The area of ∆ABC = 30
2) Length of CB = 13
IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in our free video: https://www.gmatprepnow.com/module/gmat- ... cy?id=1103

Target question: What are the coordinates of point B ?

NOTE: points A and C are LOCKED in their positions. Since ∠CAB = 90º, we know that point B is SOMEWHERE along the line y = 4. So, some of the MANY possible cases are as follows:

Image

Image

Image

Notice that, for EACH different position of point B, ∆ABC has a different area and side CB has a different length.

Okay, onto the statements...
Statement 1: The area of ∆ABC = 30
As I mentioned above, for EACH different position of point B, ∆ABC has a different area.
So, knowing that the area is 30, LOCKS point B into ONE AND ONLY ONE location.
In other words, statement 1 LOCKS IN the shape/dimensions of ∆ABC, which means there must be only one location for point B.
As such, statement 1 is SUFFICIENT

Statement 2: Length of CB = 13
As I mentioned above, for EACH different position of point B, side CB has a different length.
So, knowing that side CB has length 13 LOCKS point B into ONE AND ONLY ONE location.
In other words, statement 2 LOCKS IN the shape/dimensions of ∆ABC, which means there must be only one location for point B.
As such, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

PS: Here are a few more DS Geometry questions to practice with:
- https://www.beatthegmat.com/good-ds-ques ... 70971.html
- https://www.beatthegmat.com/what-is-the- ... 74620.html
- https://www.beatthegmat.com/what-is-the- ... 77326.html
- https://www.beatthegmat.com/geometry-tri ... 71836.html
- https://www.beatthegmat.com/ds-2-t278892.html
- https://www.beatthegmat.com/coordinate-g ... 77659.html
Brent Hanneson - Creator of GMATPrepNow.com
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