### All GMAT Math Resources

## Example Questions

### Example Question #153 : Coordinate Geometry

Consider segment with midpoint at the point .

I) Point has coordinates of .

II) Segment has a length of units.

What are the coordinates of point ?

**Possible Answers:**

Either statement alone is sufficient to answer the question.

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Neither I nor II are sufficient to answer the question. More information is needed.

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

Both statements are necessary to answer the question.

**Correct answer:**

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

In this case, we are given the midpoint of a line and asked to find one endpoint.

Statement I gives us the other endpoint. We can use this with midpoint formula (see below) to find our other point.

Midpoint formula:

Statment II gives us the length of the line. However, we know nothing about its orientation or slope. Without some clue as to the steepness of the line, we cannot find the coordinates of its endpoints. You might think we can pull of something with distance formula, but there are going to be two unknowns and one equation, so we are out of luck.

So,

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

### Example Question #154 : Coordinate Geometry

Find endpoint given the following:

I) Segment has its midpoint at .

II) Point is located on the -axis, points from the origin.

**Possible Answers:**

Neither statement is sufficient to answer the question. More information is needed.

Both statements are needed to answer the question.

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Either statement is sufficient to answer the question.

**Correct answer:**

Both statements are needed to answer the question.

**Find endpoint Y given the following:**

**I) Segment RY has its midpoint at (45,65)**

**II) Point R is located on the x-axis, 13 points from the origin.**

I) Gives us the location of the midpoint of our segment

**(45,65)**

II) Gives us the location of one endpoint

**(13,0)**

Use I) and II) to work backwards with midpoint formula to find the other endpoint.

So endpoint is at .

Therefore, both statements are needed to answer the question.

### Example Question #1 : Midpoint Formula

Consider segment

I) Endpoint is located at the origin

II) has a distance of 36 units

Where is endpoint located?

**Possible Answers:**

Both statements are needed to answer the question.

Either statement is sufficient to answer the question.

Statement II is sufficient to answer the question, but Statement I is not sufficient to answer the question.

Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

**Correct answer:**

Neither statement is sufficient to answer the question. More information is needed.

To find the endpoint of a segment, we can generally use the midpoint formula; however, in this case we do not have enough information.

I) Gives us one endpoint

II) Gives us the length of DF

The problem is that we don't know the orientation of DF. It could go in infinitely many directions, so we can't find the location of without more information.

### Example Question #1 : Midpoint Formula

is the midpoint of line PQ. What are the coordinates of point P?

(1) Point Q is the origin.

(2) Line PQ is 8 units long.

**Possible Answers:**

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

EACH statement ALONE is sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

**Correct answer:**

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

The midpoint formula is

,

with statement 1, we know that Q is and can solve for P:

and

Statement 1 alone is sufficient.

Statement 2 doesn't provide enough information to solve for point P.

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