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Example Questions
Example Question #1 : Find The Distance Between Two Parallel Lines
Find the distance between the two lines.
Since the slope of the two lines are equivalent, we know that the lines are parallel. Therefore, they are separated by a constant distance. We can then find the distance between the two lines by using the formula for the distance from a point to a nonvertical line:
First, we need to take one of the line and convert it to standard form.
where
Now we can substitute A, B, and C into our distance equation along with a point, , from the other line. We can pick any point we want, as long as it is on line
. Just plug in a number for x, and solve for y. I will use the y-intercept, where x = 0, because it is easy to calculate:
Now we have a point, , that is on the line
. So let's plug
our values for
:
Example Question #21 : Gre Subject Test: Math
Find the distance between and
To find the distance, choose any point on one of the lines. Plugging in 2 into the first equation can generate our first point:
this gives us the point
We can find the distance between this point and the other line by putting the second line into the form :
subtract the whole right side from both sides
now we see that
We can plug the coefficients and the point into the formula
where
represents the point.
Example Question #3 : Find The Distance Between Two Parallel Lines
Find the distance between and
To find the distance, choose any point on one of the lines. Plugging in into the second equation can generate our first point:
this gives us the point
We can find the distance between this point and the other line by putting the second line into the form :
subtract the whole right side from both sides
multiply both sides by
now we see that
We can plug the coefficients and the point into the formula
where
represents the point.
Example Question #4 : Find The Distance Between Two Parallel Lines
How far apart are the lines and
?
To find the distance, choose any point on one of the lines. Plugging in into the first equation can generate our first point:
this gives us the point
We can find the distance between this point and the other line by putting the second line into the form :
subtract the whole right side from both sides
multiply both sides by
now we see that
We can plug the coefficients and the point into the formula
where
represents the point.
Example Question #5 : Find The Distance Between Two Parallel Lines
Find the distance between and
To find the distance, choose any point on one of the lines. Plugging in into the second equation can generate our first point:
this gives us the point
We can find the distance between this point and the other line by putting the second line into the form :
subtract the whole right side from both sides
multiply both sides by
now we see that
We can plug the coefficients and the point into the formula
where
represents the point.
Example Question #6 : Find The Distance Between Two Parallel Lines
Find the distance between and
To find the distance, choose any point on one of the lines. Plugging in into the first equation can generate our first point:
this gives us the point
We can find the distance between this point and the other line by putting the second line into the form :
subtract the whole right side from both sides
multiply both sides by
now we see that
We can plug the coefficients and the point into the formula
where
represents the point.
Example Question #11 : Distance & Midpoint Formulas
Find the distance between the lines and
To find the distance, choose any point on one of the lines. Plugging in into the first equation can generate our first point:
this gives us the point
We can find the distance between this point and the other line by putting the second line into the form :
subtract the whole right side from both sides
multiply both sides by
now we see that
We can plug the coefficients and the point into the formula
where
represents the point.
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