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 #1 : 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