# Algebra 1 : Points and Distance Formula

## Example Questions

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### Example Question #1 : How To Find The Length Of A Line With Distance Formula

Find the length of the line segment from the origin to the point (3, 4).

5

7

49

25

1

5

Explanation:

Here, we need to use the distance formula between the two points (0, 0) and (3, 4).

### Example Question #1 : How To Find The Length Of A Line With Distance Formula

I have two points, (–8,3) and (6,–1). If I want to connect those two points with a line segment, how long would that line segment need to be?

Infinite

Explanation:

To determine how long the line needs to be to connect those two points, we need to use the distance formula, shown below.

The two points are  and .  In our case, the points are (–8, 3) and (6, –1).

So in order to connect the two points, the length of the line needs to have .

### Example Question #3 : How To Find The Length Of A Line With Distance Formula

What is the distance between the points  and ?

Explanation:

To solve problems like this, we simply need to use the distance formula, . Plugging in the  and  values from our points yields , or . Solving this radical gives us a value of , or 5.

### Example Question #4 : How To Find The Length Of A Line With Distance Formula

Find the length of the line segment with endpoints at  and

None of the other answers are correct.

None of the other answers are correct.

Explanation:

Use the distance formula, with   :

Therefore, none of the integer answer choices are correct.

### Example Question #5 : How To Find The Length Of A Line With Distance Formula

Find the distance between the two points  and .

Explanation:

The distance between two points can be found with the equation . Substituting in values you get . This means that the answer is .

### Example Question #6 : How To Find The Length Of A Line With Distance Formula

Find the distance between the midpoints of line A with the points  and  and line. B with the points  and .

Explanation:

Use the midpoint formula:

Remember points are written in the following format:

Substitute for line A

The midpoint of line A is .

Substitute for line B.

The midpoint of line B is .

Now we can find the distance between these two points using the distance formula:

Substitute the using the known values for lines A and B.

Simplify.

The distance between the two midpoints of lines A and B is .

### Example Question #7 : How To Find The Length Of A Line With Distance Formula

Find the distance between the following points:

Explanation:

Use the equation to calculated the distance between two points:

where

we can find the distance.

### Example Question #1 : How To Find The Length Of A Line With Distance Formula

Find the length of the line between the two points provided using the distance formula.

Explanation:

It is definately possible to find the distance from point A to point B, given the coordinates.

We can do this by using the formula:

.

The points provided can be plugged into this formula as follows:

.

This is the length.

### Example Question #9 : How To Find The Length Of A Line With Distance Formula

Find the length of the line between the two points provided using the distance formula.

Explanation:

It is definately possible to find the distance from point A to point B, given the coordinates:

We can do this by using the formula:

.

The points provided can be plugged into this formula as follows:

.

This is the length.

### Example Question #10 : How To Find The Length Of A Line With Distance Formula

Find the length of the line between the two points provided using the distance formula.

Explanation:

It is definately possible to find the distance from point A to point B, given the coordinates:

We can do this by using the formula:

.

The points provided can be plugged into this formula as follows:

.

This is the length.

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