GMAT Math : DSQ: Calculating the length of a line with distance formula
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Example Questions
Example Question #1 : Lines
A line segment has an endpoint at 
1) Its other endpoint is
2) Its midpoint is
Given the other endpoint, you can use the distance formula to find the length of the segment:
Given the midpoint, you can use the distance formula to find the distance from the first endpoint to the midpoint, then double that to get the length of the segment:
The total length is twice that, or 10.
The answer is that either statement alone is sufficient to answer the question.
Example Question #2 : Lines
Note: Figure NOT drawn to scale.
Give 
Statement 1:
Statement 2:
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
If you know only that 
If you know only that 
If you know both facts, then you know
Example Question #3 : Distance Formula
Consider segment 
I) Point 
II) Segment 
Find the coordinates of point 
Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.
Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.
Either statement alone is sufficient to answer the question.
Neither I nor II are sufficient to answer the question. More information is needed.
Both statements are necessary to answer the question.
Neither I nor II are sufficient to answer the question. More information is needed.
Statement I gives us a point.
Statement II gives us the length of the segment.
We are asked to find the coordinates of the other end of the segment. However, we will need more information. Even with all of our information, we have no clue as to the orientation of the line. It could be 14 units straight up and down, it could be a perfectly horizontal line, or something inbetween, thus our answer is:
Neither I nor II are sufficient to answer the question. More information is needed.
Example Question #4 : Distance Formula
Find the length of Segment YZ
I) Point Y is located at the point 
II) Point Z has a y-coordinate twice that of Point Y and an x-coordinate one-third of Point Y.
Neither statement is sufficient to answer the question. More information is needed.
Either statement is sufficient to answer the question.
Both statements are needed to answer the question.
Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.
Statement II is sufficient to answer the question, but Statement I is not sufficient to answer the question.
Both statements are needed to answer the question.
To find the length of a segment, use the distance formula. The distance formula is given by the following:
Where your 
To find the length of Segment YZ, we need the endpoints.
Statement I gives you Point Y's coordinates.
Statement II relates Point Z's coordinates to Point Y's coordinates. Thus, we can find the point Z using Statement II.
Therefore, we need both.
Recap:
Find the length of Segment YZ
I) Point Y is located at the point 
II) Point Z has a y-coordinate twice that of Point Y, and an x-coordinate one-third of Point Y.
Use Statement II along with Statement I to find the coordinates of Point Z:
Then, use distance formula to find the length of Segment YZ:
Example Question #5 : Dsq: Calculating The Length Of A Line With Distance Formula
Consider segment
I) Endpoint 
Ii) Endpoint 
What is the length of 
Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.
Neither statement is sufficient to answer the question. More information is needed.
Both statements are needed to answer the question.
Either statement is sufficient to answer the question.
Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.
Both statements are needed to answer the question.
To find the length of a segment, we need both endpoints.
Statement I gives us one endpoint.
Statement II relates 
Thus, we need both. Once we have both endpoints, distance is easily calculated via the distance formula or the Pythagorean theorem.
Using Statement II, we find the second endpoint to be 
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