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Example Questions
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?
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 #52 : Lines
A line segment is drawn starting from the origin and terminating at the point . What is the length of the line segment?
Using the distance formula,
Example Question #2 : Distance Formula
What is the distance between and
?
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 #51 : Coordinate Geometry
If we graph the equation what is the distance from the y-intercept to the x-intercept?
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
.
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
.
By the distance formula
where and
we have
Example Question #61 : Coordinate Geometry
Find the length of for
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 #1 : Distance Formula
Find the length of for
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 #9 : How To Find The Length Of A Line With Distance Formula
Find the length of the line for
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 #1 : How To Find The Length Of A Line With Distance Formula
Find the length of for the interval
.
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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