# GMAT Math : Calculating the midpoint of a line segment

## 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 ?

Explanation:

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 #1 : 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.

Explanation:

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 #1 : Lines

Find the midpoint of the points and .      Explanation:

Add the corresponding points together and divide both values by 2: ### Example Question #4 : Coordinate Geometry

What is the midpoint of and ?      Explanation:

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 #1 : Midpoint Formula

Consider segment which passes through the points and .

What are the correct coordinates for the midpoint of ?      Explanation:

Midpoint formula is as follows: Plug in and calculate: ### Example Question #601 : Geometry

Segment has endpoints of and . If the midpoint of is given by point , what are the coordinates of point ?      Explanation:

Midpoints can be found using the following: Plug in our points (-6,8) and (4,26) to find the midpoint. ### Example Question #7 : Coordinate Geometry

What are the coordinates of the mipdpoint of the line segment if and       The midpoint formula is  