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

Study concepts, example questions & explanations for Intermediate Geometry

varsity tutors app store varsity tutors android store

Example Questions

← Previous 1

Example Question #56 : Lines

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?

Possible Answers:

Correct answer:

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 #57 : Lines

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

Possible Answers:

Correct answer:

Explanation:

Using the distance formula, 

Example Question #58 : Lines

What is the distance between and ?

Possible Answers:

Correct answer:

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 #59 : Lines

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

Possible Answers:

Correct answer:

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 #60 : Lines

Find the distance of the line connecting the pair of points

 and .

Possible Answers:

Correct answer:

Explanation:

By the distance formula 

where  and 

we have

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

Find the distance of the line connecting the pair of points

 and .

Possible Answers:

Correct answer:

Explanation:

By the distance formula 

where  and 

we have

Example Question #2 : How To Find The Length Of A Line With Distance Formula

Find the length of for

Possible Answers:

Correct answer:

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

Find the length of for

Possible Answers:

Correct answer:

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 add

 

 first multiply 

 then add

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

Find the length of the line for

Possible Answers:

Correct answer:

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:

add 6 to both sides

multiply by 2

this endpoint is (10, -1)

 

add 6 to both sides

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

Find the length of for the interval .

Possible Answers:

Correct answer:

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 :

← Previous 1
Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: