# Intermediate Geometry : How to find the length of a line with distance formula

## Example Questions

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### Example Question #1 : Distance Formula

A line segment begins from the origin and is 10 units long, which of the following points could NOT be an endpoint for the line segment?

Explanation:

By the distance formula, the sum of the squares of each point must add up to 10 squared. The only point that doesn't fufill this requirement is (5,9)

### Example Question #2 : Distance Formula

A line segment is drawn starting from the origin and terminating at the point .  What is the length of the line segment?

Explanation:

Using the distance formula,

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

What is the distance between and ?

Explanation:

In general, the distance formula is given by:   and is based on the Pythagorean Theorem.

Let and

So the equation to soolve becomes or

### Example Question #1 : Distance Formula

If we graph the equation  what is the distance from the y-intercept to the x-intercept?

Explanation:

First, you must figure out where the x and y intercepts lie. To do this we begin by plugging in  to our equation, giving us . Thus . So our x-intercept is the point . We then plug in , giving us , so we know our y-intercept is the point . We then use the distance formula  and plug in our points, giving us

### Example Question #1 : Distance Formula

Find the distance of the line connecting the pair of points

and .

Explanation:

By the distance formula

where  and

we have

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

Find the distance of the line connecting the pair of points

and .

Explanation:

By the distance formula

where  and

we have

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

Find the length of for

Explanation:

To find the distance, first we have to find the specific coordinate pairs that we're finding the distance between. We know the x-values, so to find the y-values we can plug these endpoint x-values into the line:

first multiply

then subtract

first multiply

then subtract

Now we know that we're finding the distance between the points and . We can just plug these values into the distance formula, using the first pair as and the second pair as . It would work either way since we are squaring these values, this just makes it easier.

### Example Question #8 : How To Find The Length Of A Line With Distance Formula

Find the length of for

Explanation:

To find the distance, first we have to find the specific coordinate pairs that we're finding the distance between. We know the x-values, so to find the y-values we can plug these endpoint x-values into the line:

first multiply

first multiply

Now we know that we're finding the distance between the points  and . We can just plug these values into the distance formula, using the first pair as and the second pair as . Note that it would work either way since we are squaring these values anyway.

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

Find the length of the line for

Explanation:

To find the distance, first we have to find the specific coordinate pairs that we're finding the distance between. We know the y-values, so to find the x-values we can plug these endpoint y-values into the line:

multiply by 2

this endpoint is (10, -1)

multiply by 2

this endpoint is (28, 8)

Now we can plug these two endpoints into the distance formula:

note that it really does not matter which pair we use as and which as since we'll be squaring these differences anyway, just as long as we are consistent.

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

Find the length of for the interval .

Explanation:

To find this length, we need to know the y-coordinates for the endpoints.

First, plug in -5 for x:

Next, plug in 10 for x:

So we are finding the distance between the points and

We will use the distance formula, . We could assign either point as and it would still work, but let's choose :

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