Bunuel wrote:
What are the coordinates of point B in the figure above ?
(1) The area of ∆ABC = 30
(2) Length of CB = 13
Kudos for a correct solution. 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
Answer: D
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