### 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 ?

**Possible Answers:**

Quadrants II and III

Quadrants II and IV

Quadrants I and III

Quadrants I and IV

Quadrants III and IV

**Correct answer:**

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 .

**Possible Answers:**

It cannot be determined from the information given.

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

Add the corresponding points together and divide both values by 2:

### Example Question #4 : Coordinate Geometry

What is the midpoint of and ?

**Possible Answers:**

**Correct answer:**

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 #5 : Coordinate Geometry

Consider segment which passes through the points and .

What are the correct coordinates for the midpoint of ?

**Possible Answers:**

**Correct answer:**

Midpoint formula is as follows:

Plug in and calculate:

### Example Question #6 : Coordinate Geometry

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

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

**Correct answer:**

The midpoint formula is