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# Coordinate Geometry Word Problems Study Guide (page 2)

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Updated on Oct 3, 2011

## Distance Formula

Another common formula used in coordinate geometry is the distance formula. To find the distance between any two points, use the formula

#### Example

What is the distance between the two points (1,6) and (–2,2)?

Read and understand the question. This question is looking for the distance between two points.

Make a plan. Use the formula and substitute the coordinates of the two points. Use (1,6) as (x1,y1) and (–2,2) as (x2,y2).

Carry out the plan. The formula becomes

Evaluate the exponents and add the squares together.

Take the square root of 25 to get a distance of 5 units.

Check your answer. To check this result, substitute the values in the opposite order to make sure that the distance is the same. The formula is

units

This result is checking.

## Midpoint Formula

The midpoint of two points is the location halfway between the points. To find the midpoint between any two points, use the formula .

#### Example

What is the midpoint between the two points (9,3) and (–5,1)?

Read and understand the question. This question is looking for the midpoint between two points.

Make a plan. Use the formula and substitute the coordinates of the two points. Use (9,3) as (x1,y1) and (–5,1) as (x2,y2).

Carry out the plan. The formula becomes. Add to get Simplify each fraction to get the midpoint of (2,2).

Check your answer. To check this result, substitute the values in the opposite order to make sure that the midpoint is the same. The formula is

This result is checking.

Find practice problems and solutions for these concepts at Coordinate Geometry Word Problems Practice Questions.

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