# GRE Subject Test: Math : Distance & Midpoint Formulas

## Example Questions

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### Example Question #31 : Calculus

Given two points,  and , find the midpoint.

Explanation:

Step 1: Define midpoint. The midpoint is a point located between two given points.. If I draw a line through these points, I get a straight line

Step 2: The midpoint formula is:

Step 3. Plug in the values:

Step 4: Simplify each fraction in Step 3:

Step 5: Convert each fraction to a decimal from step 4:

The midpoint is

### Example Question #32 : Calculus

Find the length of the line that connects the points:  and .

Explanation:

Step 1: Recall the distance formula:

Step 2: Find ...

Step 3: Substitute the values into the equation:

Reduce the parentheses:

Step 4: Reduce  into lowest terms...

Using rule of square roots, multiplying two roots with the same value on the inside just gives me the inside value..

The length of the line that connects both points is .

### Example Question #23 : Coordinate Geometry

What is the distance between  and

Explanation:

Step 1: Plug in values into the distance formula:

Step 2: Evaluate the inside...

Step 3: Simplify...

### Example Question #33 : Calculus

Find the midpoint between  and

Explanation:

To find the midpoint you must use the equation

Insert numbers

### Example Question #21 : Distance & Midpoint Formulas

Find the distance between the two points