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Concentration: Technology, Social Entrepreneurship

WE: Information Technology (Computer Software)

Re: What are the coordinates of point B in the figure above ?
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28 Aug 2015, 11:38

B(x,4); we have to find out x. 1. 1/2* 5*x=30 ; so we can find out value of x. sufficient. 2. distance between (-3,-1) and (x,4) is 13 so we will be able to find out value of x. sufficient.

Re: What are the coordinates of point B in the figure above ?
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19 May 2017, 23:15

AC and AB are perpendicular, and we can see slope of AC = (4-(-1))/(-3-(-3)) = infinity so slope of AB must be 0. Or we can say that since AC is parallel to y-axis, AB must be parallel to x-axis hence its slope must be 0.

This means the y-coordinate of point B must be same as y-coordinate of point A. Thus we can say that point B is (x,4). Our task is to find the value of x and the question is solved. If distance AB is known then also point B can be easily calculated. We also know that distance AC = 5 (apply distance formula or its just plain visible).

Statement 1. Area of a right angled triangle = 1/2 * product of two perpendicular sides. Ac is known so AB can be calculated. Thus x can be found. Sufficient.

Statement 2. Length of CB=13. This is a right angle triangle, so using Pythagoras theorem, AB can be calculated. Thus x can be found. Sufficient.

Observation 1: that the given triangle ABC is a right triangle with one of the legs AC of length 5 units [Distance between (-3,4) and (-3,-1)] Observation 2: Line AB is parallel to X-Axis so all we need is X-coordinate of point B or length of length of AC to find length of AB using pythagorus theorem

Statement 1: Area of ABC = 30 i.e. (1/2)*AB*AC = 30 i.e. (1/2)*AB*5 = 30 i.e. AB = 12 SUFFICIENT

Statement 2: BC=13 Using pythagorus theorem we find that AB = 12 SUFFICIENT

Answer: Option D
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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 the video below.

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:

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