# GED Math : Distance Formula

## Example Questions

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### Example Question #126 : Coordinate Geometry

Use the distance formula to calculate the distance between the points and .

Explanation:

The distance between 2 points can be determined using the distance formula:

### Example Question #127 : Coordinate Geometry

Find the distance between the following two points:

Explanation:

To find the distance we need to use the distance formula:

Plug in your x and y values to get:

Combine like terms to get:

Continue with your order of operations:

Don't forget to simplify if possible:

### Example Question #128 : Coordinate Geometry

Find the distance between these two points:

Explanation:

For this problem we must use the distance formula:

Plug in your x and y values:

Combine like terms:

This cannot be simplified so you are left with the correct answer.

### Example Question #1 : Distance Formula

Find the distance between the two following points:

Explanation:

We must use the distance formula to solve this problem:

Plug in your x and y values:

Combine like terms:

Continue with your order of operations

Simplify to get:

### Example Question #130 : Coordinate Geometry

What is the distance between the points  and ?

Explanation:

Write the distance formula.

Substitute the points into the formula.

Factor the radical using factors of perfect squares.

### Example Question #1 : Distance Formula

Find the distance from point  to .

Explanation:

Write the formula to find the distance between two points.

Substitute the points into the radical.

### Example Question #2 : Distance Formula

What is the distance between  and ?

Explanation:

Write the distance formula.

Substitute the points into the equation.

### Example Question #3 : Distance Formula

Use distance formula to find the distance between the following two points.

Explanation:

Use distance formula to find the distance between the following two points.

Distance formula is as follows:

Note that it doesn't matter which point is "1" and which point is "2" just so long as we remain consistent.

So, let's plug and chug.

### Example Question #4 : Distance Formula

A triangle on a coordinate plane has the following vertices: . What is the perimeter of the triangle?

Explanation:

Since we are asked to find the perimeter of the triangle, we will need to use the distance formula to find the length of each side. Recall the distance formula:

Start by finding the distance between the points :

Next, find the distance between .

Then, find the distance between .

Finally, add up the lengths of each side to find the perimeter of the triangle.

### Example Question #5 : Distance Formula

Find the distance between the points  and .

Explanation:

Find the distance between the points  and .

To find the distance between two points, we will use distance formula (clever name). Distance formula can be thought of as a modified Pythagorean Theorem. What distance formula does is essentially treats our two points as the ends of a hypotenuse on a right triangle, then uses the two side lengths to find the hypotenuse.

Distance formula:

Pythagorean Theorem

If the connection isn't clear, don't worry, we can still solve for distance.