DSQ: Calculating the midpoint of a line segment - GMAT Quantitative Reasoning
Card 0 of 5
In what quadrant or axis is the midpoint of the line segment with endpoints 
and 
located?
Statement 1: 
Statement 2: 
is in Quadrant IV.
In what quadrant or axis is the midpoint of the line segment with endpoints
Statement 1:
Statement 2:
The midpoint of the segment with endpoints 
and 
is 
.
If 
, then 
and 
, so the midpoint, having both of its coordinates positive, is in Quadrant I.
If 
is in Quadrant IV, then 
and 
. But the quadrant of the midpoint varies according to 
and 
:
Example 1: If 
, the midpoint is 
, or 
, putting it in Quadrant I.
Example 2: If 
, the midpoint is 
, or 
, putting it in Quadrant III.
Therefore, the first statement, but not the second, tells us all we need to know.
The midpoint of the segment with endpoints
If
If
Example 1: If
Example 2: If
Therefore, the first statement, but not the second, tells us all we need to know.
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A line segment has one of its endpoints at 
. In which quadrant, or on what axis, is its other endpoint?
Statement 1: The midpoint of the segment is 
.
Statement 2: The length of the segment is 10.
A line segment has one of its endpoints at
Statement 1: The midpoint of the segment is
Statement 2: The length of the segment is 10.
Statement 1 give us the means to find the other endpoint using the midpoint formula:
Similarly,
This makes the endpoint 
, which is in Quadrant I.
Statement 2 is also sufficient. 
, which is in Quadrant 1, is 12 units away from the nearest axis; since the length of the segment is 10, the entire segment must be in Quadrant I.
Statement 1 give us the means to find the other endpoint using the midpoint formula:
Similarly,
This makes the endpoint
Statement 2 is also sufficient.
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Consider segment 
. What are the coordinates of the midpoint of 
?
I) Point 
has coordinates of 
.
II) Point 
has coordinates of 
.
Consider segment
I) Point
II) Point
We are asked to find the midpoint of a line segment and given endpoints in our clues.
Midpoint formula is found by taking the average of the x and y values of two points.
We need both endpoints to solve this problem, so both statements are needed.
We are asked to find the midpoint of a line segment and given endpoints in our clues.
Midpoint formula is found by taking the average of the x and y values of two points.
We need both endpoints to solve this problem, so both statements are needed.
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Find the midpoint of segment 
given that point 
is at 
.
I) The 
coordinate of 
is twice that of 
, and the 
coordinate of 
is 
that of 
.
II) 
is 
units long.
Find the midpoint of segment
I) The
II)
To find the midpoint, we need to know both endpoints.
I) Gives us the means to find out other endpoint.
II) Gives us the length of PS, but we are not given any hint as to its orientation.Thus, we cannot find the other endpoint and we cannot find the midpoint.
Thus, Statement I alone is sufficient to answer the question.
To find the midpoint, we need to know both endpoints.
I) Gives us the means to find out other endpoint.
II) Gives us the length of PS, but we are not given any hint as to its orientation.Thus, we cannot find the other endpoint and we cannot find the midpoint.
Thus, Statement I alone is sufficient to answer the question.
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Find the midpoint of segment 
.
I) Endpoint 
has coordinates of 
.
II) Endpoint 
coordinate is half of 
, and 
coordinate is one sixteenth of 
coordinate.
Find the midpoint of segment
I) Endpoint
II) Endpoint
To find the midpoint of a segment we need both endpoints
I) Gives us one endpoint.
II) Gives us clues to find the other endpoint.
has coordinates of 
Use midpoint formula
To find the midpoint of a segment we need both endpoints
I) Gives us one endpoint.
II) Gives us clues to find the other endpoint.
Use midpoint formula
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