Precalculus : Distance

Study concepts, example questions & explanations for Precalculus

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Example Questions

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Example Question #21 : Gre Subject Test: Math

Find the distance between and the point

Possible Answers:

Correct answer:

Explanation:

To find the distance, use the formula where the point is and the line is

First, we'll re-write the equation  in this form to identify , , and :

subtract from and add  to both sides

 multiply both sides by 

 Now we see that . Plugging these plus  into the formula, we get:

Example Question #1 : Find The Distance Between Two Parallel Lines

Find the distance  between the two lines.

Possible Answers:

Correct answer:

Explanation:

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 #2 : Find The Distance Between Two Parallel Lines

Find the distance between and

Possible Answers:

Correct answer:

Explanation:

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

Possible Answers:

Correct answer:

Explanation:

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 ?

Possible Answers:

Correct answer:

Explanation:

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

Possible Answers:

Correct answer:

Explanation:

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 

Possible Answers:

Correct answer:

Explanation:

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 #7 : Find The Distance Between Two Parallel Lines

Find the distance between the lines and

Possible Answers:

Correct answer:

Explanation:

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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