All GMAT Math Resources
Example Questions
Example Question #1 : Coordinate Geometry
Which of the following quadrants can contain the midpoint of a line segment with endpoints and for some nonzero value of ?
Quadrants I and III
Quadrants III and IV
Quadrants I and IV
Quadrants II and III
Quadrants II and IV
Quadrants II and IV
The midpoint of the line segment with endpoints and is , or
If , then the -coordinate is negative and the -coordinate is positive, so the midpoint is in Quadrant II. If , the reverse is true, so the midpoint is in Quadrant IV.
Example Question #2 : Coordinate Geometry
The midpoint of a line segment with endpoints and is . Sove for .
It cannot be determined from the information given.
It cannot be determined from the information given.
The midpoint of a line segment with endpoints is
.
Substitute the coordinates of the endpoints, then set each equation to the appropriate midpoint coordinate.
-coordinate:
-coordinate:
Simplify each, then solve the system of linear equations in two variables:
The two linear equations turn out to be equivalent, meaning that there are infinitely many solutions to the system. Therefore, insufficient information is given to answer the question.
Example Question #3 : Coordinate Geometry
Find the midpoint of the points and .
Add the corresponding points together and divide both values by 2:
Example Question #4 : Coordinate Geometry
What is the midpoint of and ?
Add the x-values and divide by 2, and then add the y-values and divide by 2. Be careful of the negatives!
Example Question #4 : Coordinate Geometry
Consider segment which passes through the points and .
What are the correct coordinates for the midpoint of ?
Midpoint formula is as follows:
Plug in and calculate:
Example Question #4 : Coordinate Geometry
Segment has endpoints of and . If the midpoint of is given by point , what are the coordinates of point ?
Midpoints can be found using the following:
Plug in our points (-6,8) and (4,26) to find the midpoint.
Example Question #5 : Calculating The Midpoint Of A Line Segment
What are the coordinates of the mipdpoint of the line segment if and
The midpoint formula is
Example Question #1 : Calculating The Endpoints Of A Line Segment
The quadrilateral with vertices is a trapezoid. What are the endpoints of its midsegment?
The midsegment of a trapezoid is the segment whose endpoints are the midpoints of its legs - its nonparallel opposite sides. These two sides are the ones with endpoints and . The midpoint of each can be found by taking the means of the - and -coordinates:
The midsegment is the segment that has endpoints (2,2) and (19,2)
Example Question #2 : Calculating The Endpoints Of A Line Segment
The midpoint of a line segment with endpoints and is . What is ?
It cannot be determined from the information given.
If the midpoint of a line segment with endpoints and is , then by the midpoint formula,
and
.
The first equation can be simplified as follows:
or
The second can be simplified as follows:
or
This is a system of linear equations. can be calculated by subtracting:
Example Question #3 : Calculating The Endpoints Of A Line Segment
If the midpoint of is and is at , what are the coordinates of ?
Midpoint formula is as follows:
In this case, we have x,y and the value of the midpoint. We need to findx' and y'
V is at (2,9) and the midpoint is at (6,7)
and
So we have (10,5) as point U