# Precalculus : Graphing Functions

## Example Questions

### Example Question #4 : Find The Distance Between A Point And A Line

Find the distance between point  to the line .

Explanation:

Distance cannot be a negative number.  The function  is a vertical line. Subtract the value of the line to the x-value of the given point to find the distance.

### Example Question #5 : Find The Distance Between A Point And A Line

Find the distance between point  to line .

Explanation:

The line  is vertical covering the first and fourth quadrant on the coordinate plane.

The x-value of  is negative one.

Find the perpendicular distance from the point to the line by subtracting the values of the line and the x-value of the point.

Distance cannot be negative.

### Example Question #6 : Find The Distance Between A Point And A Line

How far apart are the line and the point ?

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 a, b, and c:

subtract half x and add 3 to both sides

multiply both sides by 2

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

### Example Question #7 : Find The Distance Between A Point And A Line

How far apart are the line and the point ?

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 a, b, and c:

add to and subtract 8 from both sides

multiply both sides by 3

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

### Example Question #8 : Find The Distance Between A Point And A Line

Find the distance between and .

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 :

multiply both sides by

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

### Example Question #9 : Find The Distance Between A Point And A Line

Find the distance between and

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  and  from both sides

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

### Example Question #10 : Find The Distance Between A Point And A Line

Find the distance between and

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 #21 : Gre Subject Test: Math

Find the distance between and the point

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.

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

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.