Find the distance between each pair of parallel lines.

Question

y=-5x and y=-5x+26

Answer 1

Hi Hailey from Hayti, SD...hope you had a great day at school.

Glad you contacted Wyzant...I am here to help.

I will help you understand how to set these problems up and help you understand how to answer these problems. Here we do:

For first of all, do you understand what it means to satisfy the coordinates of an ordered pair?  Do you understand that for each value of x, put into the equation, there is a specific value for y. If I have an equation that is

like x + 2 = y. What that means is x is a certain value, when we substitute it in the equation, it will give you the y value. Let's try x = 3, so

putting it into the equations:

      x + 2 = y  and when x = 3, substitute then, 3 + 2 = 5   y = 5,

                     so the coordinates are    (3,5)

       Now, your turn, try it when x = 7, what would y be.

Now, with the information I have given you, you have 2 equations:

   y = -5x  substitute a value for x, what would y be (x,y) = (_,_)⇒(x₁,y₁)

           This would be only one point on one of the parallel lines

Now, the same way, with the other equation:

     y = 5x + 26, if x is some value, what would y be (x,y) = (_,_)⇒(x₂,y₂)

After you have calculate 2 coordinate points, then you use the coordinate Distance formula to calculate the distance between (x₁,y₁) & (x₂,y₂)

 

Distance between 2 coordinate points formula:

 Distance between 2 coordinate points = √(x₂ - x₁)² + (y₂ - y₁)²

    This how you solve this problem.

Once you understand how these kind of problems need to be set up, you will be a pro at them.

Contact me on Wyzant if you need any further help.

 

 

Answer 2

The guided solution follows in the procedure you must take. 

 

1.) Given two parallel straight lines, a family of perpendicular intersecting lines exists. Choose a convenient line belonging to that family passing through the origin.

 

2.) Use the coordinates of the origin in the two point form of the equation of a line to solve for the coordinates of a point corresponding to the point just used. This point is a reference point to be used to solve the formula for the distance from a point to a line, or from a line to a point on the shortest perpendicular path between them.

 

3.) The solution should be positive distance [5(26^1/2)]/13